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MitoPedia: Ergodynamics
 MitoPedia  highresolution terminology  matching measurements at highresolution.
The MitoPedia terminology is developed continuously in the spirit of Gentle Science.
 What is ergodynamics?
 New in MitoPedia: International Union of Pure and Applied Chemistry, IUPAC
Term  Abbreviation  Description 

Acceleration  a, g [m·s^{2}]  Acceleration, a, is the change of velocity over time [m·s^{2}].
a = dv/dtThe symbol g is used for acceleration of free fall. The standard acceleration of free fall is defined as g_{n} = 9.80665 [m·s^{2}]. 
Activity  a  The activity (relative activity) is a dimensionless quantity related to the concentration or partial pressure of dissolved substances. The activity of a dissolved substance B equals the concentration, c_{B} [mol·L^{1}], at high dilution divided by the unit concentration, c° = 1 mol·L^{1}:
a_{B} = c_{B}/c° This simple relationship applies frequently to substances at high dilutions <10 mmol·L^{1} (<10 mol·m^{3}). In general, the concentration of a solute has to be corrected for the activity coefficient (concentration basis), γ_{B}, a_{B} = γ_{B}·c_{B}/c° At high dilution, γ_{B} = 1. For a dissolved gas G, the activity is the partial pressure, p_{G} [Pa] (strictly: fugacity), divided by the unit partial pressure, p° = 1 Pa. The partial pressure is related to the concentration of the gas by the solubility, S_{G} [Pa/mol] (see Oxygen solubility): a_{G} = c_{G}·S_{G}/p° In general, the relative activity is defined by the chemical potential, µ_{X} a_{X} = exp[(µ_{X}µ°)/RT] 
Advancement  d_{tr}ξ [MU]  In an isomorphic analysis, any form of flow is the advancement of a process per unit of time, expressed in a specific motive unit [MU∙s^{1}], e.g., ampere for electric flow or current, I_{el} = d_{el}ξ/dt [A≡C∙s^{1}], watt for thermal or heat flow, I_{th} = d_{th}ξ/dt [W≡J∙s^{1}], and for chemical flow of reaction, I_{r} = d_{r}ξ/dt, the unit is [mol∙s^{1}] (extent of reaction per time). The corresponding motive forces are the partial exergy (Gibbs energy) changes per advancement [J∙MU^{1}], expressed in volt for electric force, Δ_{el}F = ∂G/∂_{el}ξ [V≡J∙C^{1}], dimensionless for thermal force, Δ_{th}F = ∂G/∂_{th}ξ [J∙J^{1}], and for chemical force, Δ_{r}F = ∂G/∂_{r}ξ, the unit is [J∙mol^{1}], which deserves a specific acronym [Jol] comparable to volt [V]. For chemical processes of reaction (spontaneous from highpotential substrates to lowpotential products) and compartmental diffusion (spontaneous from a highpotential compartment to a lowpotential compartment), the advancement is the amount of motive substance that has undergone a compartmental transformation [mol]. The concept was originally introduced by De Donder [1]. Central to the concept of advancement is the stoichiometric number, ν_{i}, associated with each motive component i (transformant [2]).
In a chemical reaction, r, the motive entity is the stoichiometric amount of reactant, d_{r}n_{i}, with stoichiometric number ν_{i}. The advancement of the chemical reaction, d_{r}ξ [mol], is defined as, d_{r}ξ = d_{r}n_{i}·ν_{i}^{1} The flow of the chemical reaction, I_{r} [mol·s^{1}], is advancement per time, I_{r} = d_{r}ξ·dt^{1} This concept of advancement is extended to compartmental diffusion and the advancement of charged particles [3], and to any discontinuous transformation in compartmental systems [2], 
Advancement per volume  d_{tr}Y [MU∙L^{1}]  Advancement per volume or volumespecific advancement, d_{tr}Y, is related to advancement of a transformation, d_{tr}Y = d_{tr}ξ∙V^{1} [MU∙L^{1}]. Compare d_{tr}Y with the amount of substance j per volume, c_{j} (concentration), related to amount, c_{j} = n_{j}∙V^{1} [mol∙V^{1}]. Advancement per volume is particularly introduced for chemical reactions, d_{r}Y, and has the dimension of concentration (amount per volume [mol∙L^{1}]). In an open system at steadystate, however, the concentration does not change as the reaction advances. Only in closed systems and isolated systems, specific advancement equals the change in concentration divided by the stoichiometric number,
d_{r}Y = dc_{j}/ν_{j} (closed system) d_{r}Y = d_{r}c_{j}/ν_{j} (general) With a focus on internal transformations (i; specifically: chemical reactions, r), dc_{j} is replaced by the partial change of concentration, d_{r}c_{j} (a transformation variable or process variable). d_{r}c_{j} contributes to the total change of concentration, dc_{j} (a system variable or variable of state). In open systems at steadystate, d_{r}c_{j} is compensated by external processes, d_{e}c_{j} = d_{r}c_{j}, exerting an effect on the total concentration change of substance j, dc_{j} = d_{r}c_{j} + d_{e}c_{j} = 0 (steady state)dc_{j} = d_{r}c_{j} + d_{e}c_{j} (general) 
Affinity of reaction  A [J·mol^{1}]  The concept of affinity and hence chemical force is deeply rooted in the notion of attraction (and repulsion) of alchemy, which was the foundation of chemistry originally, but diverted away from laboratory experiments towards occult secret societies [1].^{**} Newton's extensive experimental alchemical work and his substantial written track record on alchemy (which he did not publish) is seen today as a key inspiration for his development of the concept of the gravitational force [24]. This marks a transition of the meaning of affinity, from the descriptive 'adjacent' (proximity) to the causative 'attractive' (force) [5]. Correspondingly, Lavoisier (1790) equates affinity and force [6]: “... the degree of force or affinity with which the acid adheres to the base” [5]. By discussing the influence of electricity and gravity on chemical affinity, Liebig (1844) considers affinity as a force [7]. This leads to Guldberg and Waage's mass action ratio ('Studies concerning affinity', 1864; see [5]), the free energy and chemical affinity of Helmholtz (1882 [8]), and chemical thermodynamics of irreversible processes [9], where fluxforce relations are center stage [10].
According to the IUPAC definition, the affinity of reaction, A [J·mol^{1}], equals the negative molar Gibbs energy of reaction [11], which is the negative Gibbs force of reaction (derivative of Gibbs energy per advancement of reaction [12]): A = Δ_{r}F = ∂G/∂_{r}ξThe historical account of affinity is summarized by concluding, that today affinity of reaction should be considered as an isomorphic motive force and be generalized as such. This will help to (1) avoid confusing reversals of sign conventions (repulsion = negative attraction; pull = negative push), (2) unify symbols across classical and nonequilibrium thermodynamics [12,13], and thus (3) facilitate interdisciplinary communication by freeing ourselves from the alchemical, arcane scientific nomenclature. 
Amount of substance  n [mol]  The amount of substance, n, is a base physical quantity, and the corresponding SI unit is the mole [mol]. Amount of substance (sometimes abbreviated as 'amount' or 'chemical amount') is proportional to the number of specified elementary entities, N_{i} of that substance i, and the universal proportionality constant is the reciprocal value of the Avogadro constant [1],
n_{i} = N_{i}/N_{A} n_{i} contained in a system can change due to internal and external transformations, dn_{i} = d_{i}n_{i} + d_{e}n_{i} In the absence of nuclear reactions, the amount of any atom is conserved, e.g., for carbon d_{i}n_{C} = 0. This is different for chemical substances or ionic species which are produced or consumed during the advancement of a reaction, r, A change in the amount of i, dn_{i}, in an open system is due to both the internal formation in chemical transformations, d_{r}n_{i}, and the external transfer, d_{e}n_{i}, across the system boundaries. dn_{i} is positive if i is formed as a product of the reaction within the system. d_{e}n_{i} is negative if i flows out of the system and appears as a product in the surroundings [2]. 
Ampere  A  The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10^{−19} when expressed in the unit C, which is equal to A s, where the second is defined in terms of Δν_{Cs}. 
Avogadro constant  N_{A} [x·mol^{1}]  The Avogadro constant, N_{A}, has the SI unit [mol^{1}] (IUPAC), but more strictly the units for particles per amount is [x·mol^{1}] (compare Elementary charge). Therefore, the reciprocal of the Avogadro constant is the proportionality factor between the amount of substance and the number of specified elementary entities of that substance. The Avogadro constant times elementary charge is the Faraday constant. 
Barometric pressure  p_{b} [Pa]  Barometric pressure, p_{b}, is an important variable measured for calibration of oxygen sensors in solutions equilibrated with air. The atmstandard pressure (1 atm = 760 mmHg = 101.325 kPa) has been replaced by the SI standard pressure of 100 kPa. The partial pressure of oxygen, p_{O2}, in air is a function of barometric pressure, which changes with altitude and locally with weather conditions. The partial oxygen pressure declines by 12% to 14% per 1,000 m up to 6,000 m altitude, and by 15% to 17% per 1,000 m between 6,000 and 9,000 m altitude. The O2kBarometric Pressure Transducer is built into the Oroboros O2k as a basis for accurate air calibrations in highresolution respirometry. For highestlevel accuracy of calculation of oxygen pressure, it is recommended to compare at regular intervals the barometric pressure recording provided by the O2k with a calibrated barometric pressure recording at an identical time point and identical altitude. The concept of gas pressure or barometric pressure can be related to the generalized concept of isomorphic pressure. 
Boltzmann constant  k [J·x^{1}·K^{1}]  The Boltzmann constant, k, has the SI unit [J·K^{1}] (IUPAC), but more strictly the units for energy per particles per temperature is [J·x^{1}·K^{1}] (compare Gas constant). 
Bound energy  B [J]  The bound energy change in a closed system is that part of the total energy change that is always bound to an exchange of heat,
dB = dU  dA [Eq. 1] ∆B = ∆H  ∆G [Eq. 2] The free energy change (Helmoltz or Gibbs; dA or dG) is the total energy change (total inner energy or enthalpy, dU or dH) of a system minus the bound energy change. Therefore, if a process occurs at equilibrium, when dG = 0 (at constant gas pressure), then dH = dB, and at d_{e}W = 0 (dH = d_{e}Q + d_{e}W; see energy) we obtain the definition of the bound energy as the heat change taking place in an equilibrium process (eq), dB = T∙dS = d_{e}Q_{eq} [Eq. 3] 
Calorespirometric ratio  CR ratio [kJ/mol]  The calorimetric/respirometric or calorespirometric ratio (CR ratio) is the ratio of calorimetrically and respirometrically measured heat and oxygen flux, determinded by calorespirometry. The experimental CR ratio is compared with the theoretically derived oxycaloric equivalent, and agreement in the range of 450 to 480 kJ/mol O_{2} indicates a balanced aerobic energy budget (Gnaiger and Staudigl 1987). In the transition from aerobic to anaerobic metabolism, there is a limiting p_{O2}, p_{lim}, below which CR ratios become more exothermic since anaerobic energy flux is switched on. 
Candela  cd  The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10^{12} Hz, K_{cd}, to be 683 when expressed in the unit lm W^{−1}. 
Cell ergometry  Biochemical cell ergometry aims at measurement of J_{O2max} (compare V_{O2max} or V_{O2peak} in exercise ergometry of humans and animals) of cell respiration linked to phosphorylation of ADP to ATP. The corresponding OXPHOS capacity is based on saturating concentrations of ADP, [ADP]*, and inorganic phosphate, [Pi]*, available to the mitochondria. This is metabolically opposite to uncoupling respiration, which yields ETcapacity. The OXPHOS state can be established experimentally by selective permeabilization of cell membranes with maintenance of intact mitochondria, titrations of ADP and P_{i} to evaluate kinetically saturating conditions, and establishing fuel substrate combinations which reconstitute physiological TCA cycle function. Uncoupler titrations are applied to determine the apparent ETpathway excess over OXPHOS capacity and to calculate OXPHOS and ETcoupling efficiency , j_{≈P} and j_{≈E}. These normalized flux ratios are the basis to calculate the ergometric or ergodynamic efficiency, ε = j · f, where f is the normalized force ratio. » MiPNet article  
Charge number  z  The charge number of an ion or electrochemical reaction is the charge divided by the elementary charge of the ion or of electrons transferred in the reaction as defined in the reaction equation. z is a positive integer. z_{B} = Q_{B}·e^{1} 
Chemical potential  µ_{B} [J/mol]  The chemical potential of a substance B, µ_{B} [J/mol], is the partial derivative of Gibbs energy, G [J], per amount of B, n_{B} [mol], at constant temperature, pressure, and composition other than that of B,
µ_{B} = (∂G/∂n_{B})_{T,p,nj≠B} The chemical potential of a solute in solution is the sum of the standard chemical potential under defined standard conditions and a concentration (activity)dependent term, µ_{B} = µ_{B}° + RT ln(a_{B})The standard state for the solute is refered to ideal behaviour at standard concentration, c° = 1 mol/L, exhibiting infinitely diluted solution behaviour [1]. µ_{B}° equals the standard molar Gibbs energy of formation, Δ_{f}G_{B}° [kJ·mol^{1}]. The formation process of B is the transformation of the pure constituent elements to one mole of substance B, with all substances in their standard state (the most stable form of the element at 100 kPa (1 bar) at the specified temperature) [2]. 
Closed system  A closed system is a system with boundaries that allow external exchange of energy (heat and work), but do not allow exchange of matter. A limiting case is light and electrons which cross the system boundary when work is exchanged in the form of light or electric energy. If the surroundings are maintained at constant temperature, and heat exchange is rapid to prevent the generation of thermal gradients, then the closed system is isothermal. A frequently considered case are closed isothermal systems at constant pressure (and constant volume with aqueous solutions). Changes of closed systems can be partitioned according to internal and external sources. Closed systems may be homogenous (well mixed and isothermal), continuous with gradients, or discontinuous with compartments (heterogenous).  
Concentration  c [mol·L^{1}]  Concentration or density is a volumespecific quantity, expressing the number of particles as number per volume, or as properties of the particles in a variety of formats (amount, charge, mass, volume or energy per volume of the system). In chemistry, amount concentration is amount per volume, c_{B} = [B] = n_{B}·V^{1} [mol·m^{3}]. The standard concentration, c°, is defined as 1 mol·dm^{3} = 1 mol·L^{1} = 1 M.
Concentration {quote}: 1. Group of four quantities characterizing the composition of a mixture with respect to the volume of the mixture (mass, amount, volume and number concentration). 2. Short form for amount (of substance) concentration (substance concentration in clinical chemistry). {end of quote: IUPAC Gold Book} A change of concentration of an elementary entity, i, in a system, dc_{i}, can be due to internal transformations (advancement per volume, 
Density  ρ, C, D  Density is frequently a quantity divided by volume: mass density or mass concentration is mass per volume, M·V^{1} [kg·m^{3}]; radiant energy density is radiant energy per volume, Q·V^{1} [J·m^{3}]; charge density is charge per volume, Q·V^{1} [C·m^{3}]. However, electric current density is current divided by area, j=I·A^{1} [C·m^{2}]. Number density of entities or number concentration is numbers per volume, C_{B} = N_{B}·V^{1} [x·m^{3}]. In contrast, the amountofsubstance concentration, c_{B} = n_{B}·V^{1} [mol·m^{3}] is not called a substance density (IUPAC). Thus the sample mass concentration is C_{mX} = m_{X}·V^{1} [kg·m^{3}], the mitochondrial concentration is C_{mtE} = mtE·V^{1} [mtEU·m^{3}], whereas the specific mitochondrial density is D_{mtE} = mtE·m_{X}^{1} [mtEU·kg^{1}], and the mitochondrial content per object X is mtE_{NX} = mtE·N_{X}^{1} [mtEU·x^{1}] (Gnaiger 2019 MitoFit Preprint Arch). 
Discontinuous system  In a discontinuous system, gradients in continuous systems across the length, l, of the diffusion path [m], are replaced by differences across compartmental boundaries of zero thickness, and the local concentration is replaced by the free activity, α [mol·dm^{3}]. The length of the diffusion path may not be constant along all diffusion pathways, spacial direction varies (e.g., in a spherical particle surrounded by a semipermeable membrane), and information on the diffusion paths may even be not known in a discontinuous system. In this case (e.g., in most treatments of the protonmotive force) the diffusion path is moved from the (ergodynamic) isomorphic force term to the (kinetic) mobility term. The synonym of a discontinuous system is compartmental or discretized system. In the first part of the definition of discontinuous systems, three compartments are considered: (1) the source compartment A, (2) the sink compartment B, and (3) the internal barrier compartment with thickness l. In a twocompartmental description, a system boundary is defined of zero thickness, such that the barrier comparment (e.g., a semipermeable membrane) is either part of the system (internal) or part of the environment (external). Similarly, the intermediary steps in a chemical reaction may be explicitely considered in an ergodnamic multicomparment system; alternatively, the kinetic analysis of all intermediary steps may be collectively considered in the catalytic reaction mobility, reducing the measurement to a twocompartmental analysis of the substrate and product compartments.  
ETcoupling efficiency  j_{≈E}  The ETcoupling efficiency (EL coupling control factor) is a normalized flux ratio, j_{≈E} = ≈E/E = (EL)/E = 1L/E. j_{≈E} is 0.0 at zero coupling (L=E) and 1.0 at the limit of a fully coupled system (L=0). The background state is the LEAK state which is stimulated to ETpathway reference state by uncoupler titration. LEAK states L_{N} or L_{T} may be stimulated first by saturating ADP (State P) with subsequent uncoupler titration to State E. The ETcoupling efficiency is based on measurement of a coupling control ratio (LEAK control ratio, L/E), whereas the thermodynamic or ergodynamic efficiency of coupling between ATP production (DT phosphorylation) and oxygen consumption is based on measurement of the output/input flux ratio (~P/O_{2} ratio) and output/input force ratio (Gibbs force of phosphorylation/Gibbs force of oxidation). Biochemical coupling efficiency is either expressed as the ETcoupling efficiency, j_{≈E}, or OXPHOS coupling efficiency, j_{≈P}, obtained in a coupling control protocol (phosphorylation control protocol). » MiPNet article 
Electric current density  j [C·m^{2}]  Electric current density is current divided by area, j=I·A^{1} [C·m^{2}]. Compare: density. 
Elementary charge  e [C·x^{1}]  The elementary charge or proton charge, e, has the SI unit coulomb [C] (IUPAC), but more strictly coulomb per particle [C·x^{1}], which is also used as an atomic unit. 
Endergonic  Endergonic transformations or processes can proceed in the forward direction only by coupling to an exergonic process with a driving force more negative than the positive force of the endergonic process. The backward direction of an endergonic process is exergonic. The distinction between endergonic and endothermic processes is at the heart of ergodynamics, emphasising the concept of exergy changes, linked to the performance of work, in contrast to enthalpy changes, linked to heat or thermal processes, the latter expression being terminologically linked to thermodynamics.  
Endothermic  An energy transformation is endothermic if the enthalpy change of a closed system is positive when the process takes place in the forward direction and heat is absorbed from the environment under isothermal conditions (∆_{e}Q > 0) without performance of work (∆_{e}W = 0). The same energy transformation is exothermic if it proceeds in the backward direction. Exothermic and endothermic transformations can proceed spontaneously without coupling only, if they are exergonic.  
Energy  E; various [J]  Heat and work are forms of energy [1 cal = 4.184 J]. Energy [J] is a fundamental term that is used in physics and physical chemistry with various meanings [1]. These meanings become explicit in the following equations relating to systems at constant volume (dV = 0) or constant gas pressure (dp = 0). Energy is exchanged between a system and the environment across the system boundaries in the form of heat, d_{e}Q, total or available work, d_{et}W (or d_{et}W), and matter, d_{mat}U (or d_{mat}H) [2],
dU = (d_{e}Q + d_{et}W) + d_{mat}U ; dV = 0 [Eq. 1a] dH = (d_{e}Q + d_{e}W) + d_{mat}H ; dp = 0 [Eq. 1b] Whereas dU (or dH) describe the internalenergy change (or enthalpy change) of the system, heat and work are external energy changes (subscript e), and d_{mat}U (or d_{mat}H) are the exchange of matter expressed in internalenergy (or enthaply) equivalents. In closed systems, d_{mat}U = 0 (d_{mat}H = 0). The energy balance equation [Eq. 1] is a form of the First Law of Thermodynamics, which is the law of conservation of internalenergy (or enthalpy), stating that energy cannot be generated or destroyed: energy can only be transformed into different forms of work and heat, and transferred in the form of matter. Notably, the term energy is general and vague, since energy may be associated with either the first or second law of thermodynamics. An equally famous energy balance equation considers energy changes of the system only, in the most simple form for isothermal systems (dT = 0): dU = dA + T∙dS = dU + dB [Eq. 2a] dH = dG + T∙dS = dG + dB [Eq. 2b] The internalenergy change, dU (enthalpy change, dH) is the sum of free energy change (Helmholtz energy, dA; or Gibbs energy, dG) and bound energy change (bound energy, dB = T∙dS). The bound energy is that part of the energy change that is always bound to an exchange of heat. A third energy balance equation accounts for changes of the system in terms of irreversible internal processes (i) occuring within the system boundaries, and reversible external processes (e) of transfer across the system boundaries (at constant gas pressure), dH = d_{i}H + d_{e}H [Eq. 3a] dG = d_{i}G + d_{e}G [Eq. 3b] The energy conservation law of thermodynamics (first law) can be formulated as d_{i}H = 0 (at constant gas pressure), whereas the generally negative sign of the dissipated energy, d_{i}G ≡ d_{i}D ≤ 0, is a formulation of the second law of thermodynamics. Insertion into Eq. 3 yields, dH = d_{e}H [Eq. 4a] dG = d_{i}D + d_{e}W + d_{mat}G [Eq. 4b]When talking about energy transformations, the term energy is used in a general sense without specification of these various forms of energy. 
Enthalpy  H [J]  Enthalpy, H [J], can under conditions of constant gas pressure neither be destroyed nor created (first law of thermodynamics: d_{i}H/dt = 0). The distinction between enthalpy and internalenergy of a system is due to external pressurevolume work carried out reversibly at constant gas pressure. The enthalpy change of the system, dH, at constant pressure, is the internalenergy change, dU, minus reversible pressurevolume work,
dH = dU  d_{V}W Pressurevolume work, d_{V}W, at constant pressure, is the gas pressure, p [Pa = J·m^{3}], times change of volume, dV [m^{3}], d_{V}W = p·dV [J] The available work, d_{e}W, is distinguished from external total work, d_{et}W, [1] d_{e}W = d_{et}W  d_{V}W The change of enthalpy of a system is due to internal and external changes, dH = d_{i}H + d_{e}H Since d_{i}H = 0 (first law of thermodynamics), the dH is balanced by exchange of heat, work, and matter, dH = (d_{e}Q + d_{e}W) + d_{mat}H ; dp = 0 The exchange of matter is expressed in enthalpy equivalents with respect to a reference state (formation, f, or combustion, c). The value of dH in an open system, therefore, depends on the arbitrary choice of the reference state. In contrast, the terms in parentheses are the sum of all (total, t) partial energy transformations, d_{t}H = (d_{e}Q + d_{e}W) A partial enthalpy change of transformation, d_{tr}H, is distinguished from the total enthalpy change of all transformations, d_{t}H, and from the enthalpy change of the system, dH. In a closed system, dH = d_{t}H. The enthalpy change of transformation is the sum of the Gibbs energy (free energy) change of transformation, d_{tr}G, and the bound energy change of transformation at constant temperature and pressure, d_{tr}B = T·dS, d_{tr}H = d_{tr}G + d_{tr}B 
Ergodynamic efficiency  ε  The ergodynamic efficiency, ε (compare thermodynamic efficiency), is a power ratio between the output power and the (negative) input power of an energetically coupled process. Since power [W] is the product of a flow and the conjugated thermodynamic force, the ergodynamic efficiency is the product of an output/input flow ratio and the corresponding force ratio. The efficiency is 0.0 in a fully uncoupled system (zero output flow) or at level flow (zero output force). The maximum efficiency of 1.0 can be reached only in a fully (mechanistically) coupled system at the limit of zero flow at ergodynamic equilibrium. The ergodynamic efficiency of coupling between ATP production (DT phosphorylation) and oxygen consumption is the flux ratio of DT phosphorylation flux and oxygen flux (P»/O_{2} ratio) multiplied by the corresponding force ratio. Compare with the OXPHOS coupling efficiency. 
Ergodynamics  Is there a need for defining ergodynamics? "Thermodynamics deals with relationships between properties of systems at equilibrium and with differences in properties between various equilibrium states. It has nothing to do with time. Even so, it is one of the most powerful tools of physical chemistry" [1]. Ergodynamics is the theory of exergy changes (from the Greek word 'erg' which means work). Ergodynamics includes the fundamental aspects of thermodynamics ('heat') and the thermodynamics of irreversible processes (TIP; nonequilibrium thermodynamics), and thus links thermodynamics to kinetics. In its most general scope, ergodynamics is the science of energy transformations. Classical thermodynamics includes open systems, yet as a main focus it describes closed systems, which is reflected in a nomenclature that is not easily applicable to the more general case of open systems [2]. At present, IUPAC recommendations [3] fall short of providing adequate guidelines for describing energy transformations in open systems.  
Exergonic  Exergonic transformations or processes can spontaneously proceed in the forward direction, entailing the irreversible loss of the potential to performe work (erg) with the implication of a positive internal entropy production. Ergodynamic equilibrium is obtained when an exergonic (partial) process is compensated by a coupled endergonic (partial) process, such that the Gibbs energy change of the total transformation is zero. Final thermodynamic equilibrium is reached when all exergonic processes are exhausted and all forces are zero. The backward direction of an exergonic process is endergonic. The distinction between exergonic and exothermic processes is at the heart of ergodynamics, emphasising the concept of exergy changes, linked to the performance of work, in contrast to enthalpy changes, linked to heat or thermal processes, the latter expression being terminologically linked to thermodynamics.  
Exothermic  An energy transformation is exothermic if the enthalpy change of a closed system is negative when the process takes place in the forward direction and heat is lost to the environment under isothermal conditions (∆_{e}Q < 0) without performance of work (∆_{e}W = 0). The same energy transformation is endothermic if it proceeds in the backward direction. Exothermic and endothermic transformations can proceed spontaneously without coupling only, if they are exergonic.  
Extensive quantity  Extensive quantities pertain to a total system, e.g. oxygen flow. An extensive quantity increases proportional with system size. The magnitude of an extensive quantity is completely additive for noninteracting subsystems, such as mass or flow expressed per defined system. The magnitude of these quantities depends on the extent or size of the system (Cohen et al 2008).  
External flow  I_{e} [MU·s^{1}]  External flows across the system boundaries are formally reversible. Their irreversible facet is accounted for internally as transformations in a heterogenous system (internal flows, I_{i}). 
Faraday constant  F [C/mol]  The Faraday constant, F, links the electric charge [C] to amount [mol], and thus relates the electrical format, e [C], to the molar format, n [mol]. The Farady constant, F = e·N_{A} = 96,485.33 C/mol, is the product of elementary charge, e = 1.602176634∙10^{19} C/x, and the Avogadro constant, N_{A} = 6.02214076∙10^{23} x/mol. The dimensionless unit [x] is not explicitely considered by IUPAC. 
Flow  I [MU∙s^{1}]  In an isomorphic analysis, any form of flow, I is the advancement of a process per unit of time, expressed in a specific motive unit [MU∙s^{1}], e.g., ampere for electric flow or current [A≡C∙s^{1}], watt for heat flow [W≡J∙s^{1}], and for chemical flow the unit is [mol∙s^{1}]. Flow is an extensive quantity. The corresponding isomorphic forces are the partial exergy (Gibbs energy) changes per advancement [J∙MU^{1}], expressed in volt for electric force [V≡J∙C^{1}], dimensionless for thermal force, and for chemical force the unit is [J∙mol^{1}], which deserves a specific acronym ([Jol]) comparable to volt. 
Flux  J  Flux, J, is a specific quantity. Flux is flow, I [MU·s^{1} per system] (an extensive quantity), divided by system size. Flux (e.g., oxygen flux) may be volumespecific (flow per volume [MU·s^{1}·L^{1}]), massspecific (flow per mass [MU·s^{1}·kg^{1}]), or markerspecific (e.g. flow per mtEU). 
Force  F; d_{m}F_{X}; Δ_{tr}F_{X} [J·MU^{1}]  Force is an intensive quantity. The product of force times advancement is the work (exergy) expended in a process or transformation.

Format  Different formats can be chosen to express physicochemical quantities (motive entities or transformants) in corresponding motive units [MU]. Fundamental formats for electrochemical transformations are:
 
Free ETcapacity  ≈E  The Free ETcapacity, ≈E, is the ETcapacity corrected for LEAK respiration, ≈E = EL. ≈E is the respiratory capacity potentially available for ion transport and phosphorylation of ADP to ATP. Oxygen consumption in the ETpathway state, therefore, is partitioned into the free ETcapacity, ≈E, and LEAK respiration, L_{P}, compensating for proton leaks, slip and cation cycling: E = ≈E+L_{P} (see free OXPHOS capacity). 
Gas constant  R [J·mol^{1}·K^{1}]  
Heat  Q [J]  Heat is a form of energy. The relationship between heat and work provides the foundation of thermodynamics, which describes transformations from an initial to a final state of a system. In energy transformations heat may pass through the boundary of the system, at an external heat flow of d_{e}Q/dt. 
Intensive quantity  Intensive quantities are partial derivatives of an extensive quantity by the advancement, d_{tr}ξ, of an energy transformation. See: Force.  
Internal flow  I_{i} [MU·s^{1}]  Within the system boundaries, irreversible internal flows, I_{i},—including chemical reactions and the dissipation of internal gradients of heat and matter—contribute to internal entropy production, d_{i}S/dt. In contrast, external flows, I_{e}, of heat, work, and matter proceed reversibly across the system boundaries (of zero thickness). Flows are expressed in various formats per unit of time, with corresponding motive units [MU], such as chemical [mol], electrical [C], mass [kg]. Flow is an extensive quantity, in contrast to flux as a specific quantity. 
Internalenergy  U [J]  Internalenergy, U [J], can neither be destroyed nor created (first law of thermodynamics: d_{i}U/dt = 0). Note that internal (subscript i), as opposed to external (subscript e), must be distinguished from "internalenergy", U, which contrasts with "Helmholtz energy", A, as enthalpy, H, contrasts with Gibbs energy, G. 
International Union of Pure and Applied Chemistry, IUPAC  IUPAC  The International Union of Pure and Applied Chemistry (IUPAC) celebrates in 2019 the 100^{th} anniversary, which coincides with the International Year of the Periodic Table of Chemical Elements (IYPT 2019). IUPAC {quote} notes that marking Mendeleev's achievement will show how the periodic table is central to connecting cultural, economic, and political dimensions of global society “through a common language” {end of quote} [1]. 2019 is proclaimed as the International Year of the Periodic Table of Chemical Elements (IYPT 2019). For a common language in mitochondrial physiology and bioenergetics, the IUPAC Green book [2] is a most valuable resource, which unfortunately is largely neglected in bioenergetics textbooks. Integration of open systems and nonequilibrium thermodynamic approaches remains a challenge for developing a common language [3,4]. 
Isolated system  The boundaries of isolated systems are impermeable for all forms of energy and matter. Changes of isolated systems have exclusively internal origins, e.g., internal entropy production, d_{i}S/dt, internal formation of chemical species i which is produced in a reaction r, d_{i}n_{i}/dt = d_{r}n_{i}/dt. In isolated systems some internal terms are restricted to zero by various conservation laws which rule out the production or destruction of the respective quantity.  
Isomorphic  The term isomorphic refers to quantities which have identical or similar form, shape, or structure. In mathematics, an isomorphism defines a onetoone correspondence between two mathematical sets. In ergodynamics, isomorphic quantities are defined by equations of identical form. If isomorphic quantities are not expressed in identical units, then these quantities are expressed in different formats which can be converted to identical untis. Example: electric force [V=J/C] and chemical force [Jol=J/mol] are ismorphic forces; the electrical format [J/C] can be converted to the chemical format [J/mol] by the Faraday constant. In irreversible thermodynamics, isomorphic forces are referred to as generalized forces.  
Jmax  J_{max}  J_{max} is the maximum pathway flux (e.g. oxygen flux) obtained at saturating substrate concentration. J_{max} is a function of metabolic state. In hyperbolic ADP or oxygen kinetics, J_{max} is calculated by extrapolation of the hyperbolic function, with good agreement between the calculated and directly measured fluxes, when substrate levels are >20 times the c_{50} or p_{50}. 
Kelvin  K  The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10^{−23} when expressed in the unit J x^{1} K^{−1}. 
Kilogram  kg  The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10^{−34} when expressed in the unit J s, which is equal to kg m^{2} s^{−1}, where the meter and the second are defined in terms of c and Δν_{Cs}. 
LEAK control ratio  L/E  The LEAK control ratio, or L/E coupling control ratio [1,2], is the flux ratio of LEAK respiration over ETcapacity, as determined by measurement of oxygen consumption in sequentially induced states L and E of respiration. The ETpathway control ratio is an index of uncoupling or dyscoupling at constant ETcapacity. L/E increases with uncoupling from a theoretical minimum of 0.0 for a fully coupled system, to 1.0 for a fully uncoupled system [3]. 
Level flow  E  Level flow is a steady state of a system with an input process coupled to an output process (coupled system), in which the output force is zero. Clearly, energy must be expended to maintain level flow, even though output is zero (Caplan and Essig 1983; referring to zero output force, while output flow may be maximum). 
Metabolic control variable  X  A metabolic control variable, X, causes the transition between a background state, Y_{X}, and a reference state, Z_{X}. X may be a stimulator or activator of flux, inducing the step change from background to reference steady state (Y to Z). Alternatively, X may be an inhibitor of flux, absent in the reference state but present in the background state (step change from Z to Y). 
Meter  m  The meter, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s^{−1}, where the second is defined in terms of the caesium frequency Δν_{Cs}. 
Mitochondrial membrane potential  mtMP, Δψ [V]  The mitochondrial membrane potential, mtMP, is the electric part of the protonmotive force, Δp_{H+}.
Δψ = Δp_{H+}  Δµ_{H+} / F mtMP or Δψ is the potential difference across the inner mitochondrial (mt) membrane, expressed in the electric unit of volt [V]. Electric force of the mitochondrial membrane potential is the electric energy change per ‘motive’ electron or per electron moved across the transmembrane potential difference, with the number of ‘motive’ electrons expressed in the unit coulomb [C]. 
Mole  mol  The mole [mol] is the SI base unit for the amount of substance of a system that contains 6.02214076·10^{23} specified elementary entities (see Avogadro constant). The elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. 
Motive unit  MU  The motive unit [MU] is the variable SI unit in which the motive entity (transformant) of a transformation is expressed, which depends on the energy transformation under study and on the chosen format. Fundamental MU for electrochemical transformations are:
For the protonmotive force the motive entity is the proton with charge number z=1. The protonmotive force is expressed in the electrical or molar format with MU J/C=V or J/mol=Jol, respectively. The conjugated flows, I, are expressed in corresponding electrical or molar formats, C/s = A or mol/s, respectively. The charge number, z, has to be considered in the conversion of motive units (compare Table below), if a change not only of units but a transition between the entity elementary charge and an entity with charge number different from unity is involved (e.g., O_{2} with z=4). The ratio of elementary charges per O_{2} molecule (z_{O2}=4) is multiplied by the elementary charge (e, coulombs per electron), which yields coulombs per O_{2} [C∙x^{1}]. This in turn is multiplied with the Avogadro constant, N_{A} (O_{2} molecules per mole O_{2} [x∙mol^{1}]), thus obtaining for ze∙N_{A} the ratio of elementary charges [C] per amount of O_{2} [mol^{1}]. The conversion factor for O_{2} is 385.94132 C∙mmol^{1}. 
NetOXPHOS control ratio  ≈P/E  The netOXPHOS control ratio (≈P/E control ratio), ≈P/E = (PL)/E, expresses the OXPHOScapacity (corrected for LEAK respiration) as a fraction of ETcapacity. ≈P/E remains constant, if dyscoupling is fully compensated by an increase of OXPHOS capacity and free OXPHOS capacity (≈P = PL) is maintained constant. 
NetROUTINE control ratio  ≈R/E  The netROUTINE control ratio (≈R/E control ratio), ≈R/E = (RL)/E, expresses phosphorylationrelated respiration (corrected for LEAK respiration) as a fraction of ETcapacity. ≈R/E remains constant, if dyscoupling is fully compensated by an increase of ROUTINE respiration and free ROUTINE activity (≈R = RL) is maintained constant. 
Number of entities  N [x]  The number of entities, N, is different from a mere number. Whereas a number does not have a unit, a number of entities is composed of the numerical value and the countable entity, with the unit of a count [x]. Unfortunately, the dimensionless unit [x] is not explicitely considered by the SI and IUPAC (Mohr and Philipps 2015). This causes confusion, since then the unit [J] relates without discrimination to both: (1) exergy in the instrumental chamber (the system), and (2) exergy per countable entity (cells, particles, molecules, ions, electrons). The unit [J∙x^{1}] clearly indicates exergy per particle or object. The unit [x] is a motive unit. 
OXPHOS control ratio  P/E  The OXPHOS control ratio or P/E coupling control ratio (OXPHOS/ETpathway; phosphorylation system control ratio) is an expression of the limitation of OXPHOS capacity by the phosphorylation system. The relative limitation of OXPHOS capacity by the capacity of the phosphorylation system is better expressed by the excess EP capacity factor, j_{ExP} = 1P/E. The P/E ratio increases with increasing capacity of the phosphorylation system up to a maximum of 1.0 when it matches or is in excess of ETcapacity. P/E also increases with uncoupling. P/E increases from the lower boundary set by L/E (zero capacity of the phosphorylation system), to the upper limit of 1.0, when there is no limitation of P by the phosphorylation system or the proton backpressure (capacity of the phosphorylation system fully matches the ETcapacity; or if the system is fully uncoupled). It is important to separate the kinetic effect of ADP limitation from limitation by enzymatic capacity at saturating ADP concentration. » MiPNet article 
OXPHOS coupling efficiency  j_{≈P}  The OXPHOS coupling efficiency (PL or ≈P control factor), j_{≈P} = ≈P/P = (PL)/P = 1L/P. OXPHOS capacity corrected for LEAK respiration is the free OXPHOS capacity, ≈P = PL. The OXPHOS coupling efficiency is the ratio of free to total OXPHOS capacity. j_{≈P} = 1.0 for a fully coupled system (when RCR approaches infinity); j_{≈P} = 0.0 (RCR=1) for a system with zero respiratory phosphorylation capacity (≈P=0) or zero ETcoupling efficiency (EL=0 when L=P=E). If State 3 is measured at saturating ADP and P_{i} concentrations (State 3 = P), then the respiratory acceptor control ratio, RCR, is P/L. Under these conditions, the RCR and OXPHOS coupling efficiency are related by a hyperbolic function, j_{≈P} = 1RCR^{1}. » MiPNet article 
Open system  An open system is a system with boundaries that allow external exchange of energy and matter; the surroundings are merely considered as a source or sink for quantities transferred across the system boundaries (external flows, I_{ext}).  
Oxygen flow  I_{O2} [mol·s^{1}]  Respiratory oxygen flow is the oxygen consumption per total system, which is an extensive quantity. Flow is advancement of a transformation in a system per time. Oxygen flow or respiration of a cell is distinguished from oxygen flux (e.g. per mg protein or wet weight). 
Oxygen flux  J_{O2}  Oxygen flux, J_{O2}, is a specific quantity. Oxygen flux is oxygen flow, I_{O2} [mol·s^{1} per system] (an extensive quantity), divided by system size. Flux may be volumespecific (flow per volume [pmol·s^{1}·mL^{1}]), massspecific (flow per mass [pmol·s^{1}·mg^{1}]), or markerspecific (flow per mtEU). Oxygen flux (e.g., per body mass, or per cell volume) is distinguished from oxygen flow (per object, or per cell), I_{O2} [mol·s^{1}·x^{1}]. 
Oxygen pressure  p_{O2} [kPa]  Oxygen pressure or partial pressure of oxygen [kPa], related to oxygen concentration in solution by the oxygen solubility, S_{O2} [µM/kPa]. 
Oxygen solubility  S_{O2} [µM/kPa]  The oxygen solubility, S_{O2} [µM/kPa], expresses the oxygen concentration in solution in equilibrium with the oxygen pressure in a gas phase, as a function of temperature and composition of the solution. S_{O2} is 10.56 µM/kPa in pure water at 37 °C. At standard barometric pressure (100 kPa), the oxygen concentration at air saturation is 207.3 µM at 37 °C (19.6 kPa partial oxygen pressure). In MiR06 and serum, the corresponding saturation concentrations are 191 and 184 µM. The oxygen solubility depends on temperatue and the concentrations of solutes in solution. See also: Oxygen solubility factor 
PH  pH  The pH value or pH is the negative of the base 10 logarithm of the activity of protons (hydrogen ions, H^{+}). A pH electrode reports the pH and is sensitive to the activity of H^{+}. In dilute solutions, the hydrogen ion activity is approximately equal to the hydrogen ion concentration. The name pH stems from the term potentia hydrogenii. 
Pressure  P, p, Π [Pa]  Pressure [Pa = J·m^{3}] is the concentration of the force at the point of action. More generally, pressure is the force times concentration at the interphase of interaction.
In addition to mechanical pressure, hydrostatic pressure, barometric pressure, gas pressure (oxygen pressure), isomorphic pressures are distinguished as osmotic pressure, diffusion pressure, reaction pressure, and even electric pressure. In ergodynamics, the pressure in a transformation, Δ_{tr}Π, is the product of free activity times force, Δ_{tr}Π = α_{tr}·Δ_{tr}F [mol·m^{3} · J·mol^{1} = J·m^{3} = Pa]. In the classical physicochemical literature, there is confusion between the terms force and pressure: "This force is called the pressure of the gas" by Maxwell (1867); "This pressure is osmotic pressure. .. Osmotic forces are in fact .." by van't Hoff 1901; "Pressureforces" by Einstein (1905); presentation of Fick's law of diffusion (which represents a fluxpressure relationship) as a fluxforce relationship by Prigogine (1967). 
Proton  H^{+}  Proton and hydrogen ion, H+, are terms used synonymously in chemistry. A proton or hydrogen ion has no electrons and corresponds to a bare nucleus. The proton is a bare charge with only about 1/64,000 of the radius of a hydrogen atom, and so is extremely reactive chemically. The free proton has an extremely short lifetime in aqueous solutions where it forms the hydronium ion, H3O+, which in turn is further solvated by water molecules in clusters such as H_{5}O_{2}^{+} and H_{9}O_{4}^{+}.
The transfer of H^{+} in an acid–base reaction is referred to as proton transfer. The acid is the proton donor and the base is the proton acceptor. In particle physics, a proton is a subatomic particle with a positive electric charge. Protons and neutrons are collectively referred to as nucleons. 
Protonmotive force  pmF, ∆_{m}F_{H+}, Δp [J·MU^{1}]  The protonmotive force, ∆_{m}F_{H+}, is known as Δp in Peter Mitchell’s chemiosmotic theory [1], which establishes the link between electric and chemical components of energy transformation and coupling in oxidative phosphorylation. The unifying concept of the pmF ranks among the most fundamental theories in biology. As such, it provides the framework for developing a consistent theory and nomenclature for mitochondrial physiology and bioenergetics. The protonmotive force is not a vector force as defined in physics. This conflict is resolved by the generalized formulation of isomorphic, compartmental forces, ∆_{tr}F, in energy (exergy) transformations [2]. Protonmotive means that there is a potential for the movement of protons, and force is a measure of the potential for motion.
The pmF is generated in oxidative phosphorylation by oxidation of reduced fuel substrates and reduction of O_{2} to H_{2}O, driving the coupled proton translocation from the mtmatrix space across the mitochondrial inner membrane (mtIM) through the proton pumps of the electron transfer system (ETS), which are known as respiratory Complexes CI, CIII and CIV. ∆_{m}F_{H+} consists of two partial isomorphic forces: (1) The electric part, ∆_{el}F_{H+} (corresponding numerically to ∆Ψ)^{§}, is the electric potential difference^{§}, which is not specific for H^{+} and can, therefore, be measured by the distribution of any permeable cation equilibrating between the negative (matrix) and positive (external) compartment. (2) The chemical part, ∆_{d}F_{H+}, relates to the diffusion (d) of uncharged particles and contains the chemical potential difference^{§} in H+, ∆µ_{H+}, which is proportional to the pH difference, ∆pH. Motion is relative and not absolute (Principle of Galilean Relativity); likewise there is no absolute potential, but isomorphic forces are stoichiometric potential differences^{§}. The total motive force (motive = electric + chemical) is distinguished from the partial components by subscript ‘m’, ∆_{m}F_{H+}. Reading this symbol by starting with the proton, it can be seen as pmF, or the subscript m (motive) can be remembered by the name of Mitchell, ∆_{m}F_{H+} = ∆_{el}F_{H+} + ∆_{d}F_{H+} With classical symbols, this equation contains the Faraday constant, F, multiplied implicitly by the charge number of the proton (z_{H+} = 1), and has the form [1] ∆p = ∆Ψ + ∆µ_{H+}∙F^{1}A partial electric force of 0.2 V in the electrical format, ∆_{el}F_{eH+pos}, is 19 kJ∙mol^{1} H^{+}_{pos} in the molar format, ∆_{el}F_{nH+pos}. For 1 unit of ∆pH, the partial chemical force changes by 5.9 kJ∙mol^{1} in the molar format, ∆_{d}F_{nH+pos}, and by 0.06 V in the electrical format, ∆_{d}F_{eH+pos}. Considering a driving force of 470 kJ∙mol^{1} O_{2} for oxidation, the thermodynamic limit of the H^{+}_{pos}/O_{2} ratio is reached at a value of 470/19 = 24, compared to the mechanistic stoichiometry of 20 for the Npathway with three coupling sites. 
Quantity  A quantity is the attribute of a phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively.  
SI  The International System of Units  SI  The SI is a consistent system of units for use in all aspects of life, including international trade, manufacturing, security, health and safety, protection of the environment, and in the basic science that underpins all of these. The system of quantities underlying the SI and the equations relating them are based on the present description of nature and are familiar to all scientists, technologists and engineers. The definition of the SI units is established in terms of a set of seven defining constants. The complete system of units can be derived from the fixed values of these defining constants, expressed in the units of the SI. These seven defining constants are the most fundamental feature of the definition of the entire system of units. These particular constants were chosen after having been identified as being the best choice, taking into account the previous definition of the SI, which was based on seven base units, and progress in science (p. 125). 
STPD  STPD  At standard temperature and pressure dry (STPD: 0 °C = 273.15 K and 1 atm = 101.325 kPa = 760 mmHg), the molar volume of an ideal gas, V_{m}, and V_{m,O2} is 22.414 and 22.392 L∙mol^{1}, respectively. Rounded to three decimal places, both values yield the conversion factor of 0.744 from units used in spiroergometry (V_{O2max} [mL O_{2}·min^{1}]) to SI units [µmol O_{2}·s^{1}]. For comparison at normal temperature and pressure dry (NTPD: 20 °C), V_{m,O2} is 24.038 L∙mol^{1}. Note that the SI standard pressure is 100 kPa. 
Second  s  The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ∆ν_{Cs}, the unperturbed groundstate hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s^{−1}. 
Solutions  A solution is {quote}: A liquid or solid phase containing more than one substance, when for convenience one (or more) substance, which is called the solvent, is treated differently from the other substances, which are called solutes. When, as is often but not necessarily the case, the sum of the mole fractions of solutes is small compared with unity, the solution is called a dilute solution. A superscript attached to the ∞ symbol for a property of a solution denotes the property in the limit of infinite dilution {end of quote: IUPAC Gold Book}. » MiPNet article  
Specific quantity  Specific quantities are obtained when the extensive quantity is divided by system size, in contrast to intensive quantities. The adjective specific before the name of an extensive quantity is often used to mean divided by mass (Cohen et al 2008). A massspecific quantity (e.g. massspecific flux is flow divided by mass of the system) is independent of the extent of noninteracting homogenous subsystems. If massspecific oxygen flux is constant and independent of system size (expressed as mass), then there is no interaction between the subsystems. The wellestablished scaling law in respiratory physiology reveals a strong interaction of oxygen consumption and body mass by the fact that massspecific basal metabolic rate (oxygen flux) does not increase proportionally and linearly with body mass, whereas maximum massspecific oxygen flux, V_{O2max}, is constant across a large range of body mass (Weibel and Hoppeler 2005).  
Speed  v [m·s^{1}]  Speed, v [m·s^{1}], is the distance, s [m], covered by a particle per unit time, irrespective of geometrical direction in space. Therefore, speed is not a vector, in contrast to velocity. v = ds/dt [m·s^{1}] 
Static head  L  Static head is a steady state of a system with an input process coupled to an output process (coupled system), in which the output force is maximized at constant input or driving force up to a level at which the conjugated output flow is reduced to zero. In an incompletely coupled system, energy must be expended to maintain static head, even though the output is zero (Caplan and Essig 1983; referring to output flow at maximum output force). LEAK respiration is a measure of input flow at static head, when the output flow of phosphorylation (ADP>ATP) is zero at maximum phosphorylation potential (Gibbs force of phosphorylation; Gnaiger 1993a). In a completely coupled system, not only the output flux but also the input flux are zero at static head, which then is a state of ergodynamic equilibrium (Gnaiger 1993b). Whereas the output force is maximum at ergodynamic equilibrium compensating for any given input force, all forces are zero at thermodynamic equilibrium. Flows are zero at both types of equilibria, hence entropy production or power (power = flow x force) are zero in both cases, i.e. at thermodynamic equilibrium in general, and at ergodynamic equilibrium of a completely coupled system at static head. 
Stoichiometric number  ν_{X}  The sign of the stoichiometric number, ν_{X}, is determined by the direction of the transformation (positive for products, negative for substrates), and the magnitude of ν_{X} is determined by the stoichiometric form. For instance, ν_{A}=1 in the reaction 0 = 1 A + 2 B (glucose converted to 2 lactate), but ν_{A}=1/6 in the reaction 0 = 1/6 A  1 B + 1 C (1/6 glucose and O_{2} converted to H_{2}CO_{3}). 
Subscripts in physical chemistry  Subscripts in physical chemistry are used to differentiate symbols of different quantities. While these subscripts need to be short to be readable, they have to be distinct and well defined. Several subscripts relate to fundamental terms and concepts, summarized in a list below.  
System  The term system has a variety of meanings in different contexts, e.g., redox system, electron transfer system, loosely or completely coupled system, biological or mechanical system, instrumental system, data management system, MKSA system. In thermodynamics, the system is considered as an experimental system (experimental chamber), separated from the environment as an isolated, adiabatic, closed, or open system. Quote Gnaiger 1993 Pure Appl Chem: The internal domain of any system is separated from the external domain (the surroundings) by a boundary. In theory, energy transformations outside the system can be ignored when describing the system. The surroundings are merely considered as a source or sink for quantities transferred across the system boundary. According to the transfer properties of the boundary, three types of thermodynamic systems are distinguished. (1) The boundaries of isolated systems are impermeable for all forms of energy and matter. Isolated systems do not interact with the surroundings. Strictly, therefore, internal changes of isolated systems cannot be observed from outside since any observation requires interaction. (2) The boundaries of closed systems are permeable for heat and work, but impermeable for matter. A limiting case is electrons which cross the system boundary when work is exchanged in the form of electric energy [added: and light]. The volume of a closed system may be variable. (3) The boundaries of open systems allow for the transfer of heat, work and matter. Changes of isolated systems have exclusively internal origins, whereas changes of closed and open systems can be partitioned according to internal and external sources. Production and destruction of a quantity within the system are internal changes, whereas changes of heat, work and matter due to transfer across the system boundaries are labelled extenal. (External) transfer is thus contrasted with (internal) production or destruction. A system may be treated as a black box. In the analysis of continuous or discontinuous systems, however, information is implied on the internal structure of the system.  
Vector  A vector is a pysicochemical quantity with magnitude and spatial direction of a gradient. Symbols for vectors are written in bold face. For example, velocity, v, and the fundamental forces of physics, F, are vectors. An infinitesimal area is a vector, dA, perpendicular to the plane.  
Velocity  v [m·s^{1}]  Velocity, v [m·s^{1}], is the speed in a defined spatial direction, and as such velocity is a vector. Velocity is the advancement in distance per unit time, v ≡ dz ∙ dt^{1} [m·s^{1}] 
Work  d_{e}W [J]  Work [J] is a specific form of energy, called exergy, performed by a closed or open system on its surroundings (the environment). This is the definition of external work, which is zero in isolated systems. The term exergy includes external and internal work. Mechanical work is force [N] times path length [m]. The internalenergy change of a closed system, dU, is due to external exchange (e) of work and heat, and work is the internalenergy change minus heat, d_{et}W = dU  d_{e}Q 