Gnaiger 1993 Pure Appl Chem

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Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002.

» PAC, PAC:199365091983 Open Access

Gnaiger Erich (1993) Pure Appl Chem

Abstract: Important aspects of classical and nonequilibrium thermodynamics developed separately and lack alignment. Confusing definitions of heat and work exist for open systems in association with the exchange of matter. The concept of heat exchange in open systems requires clarification on the basis of calorimetric principles, whereas power is rigorously defined in terms of external work per time and the product of internal flows and forces. For illustration, analogous electric, thermal and chemical flows and forces are represented. An internal flow is the advancement of a transformation per time. A force is the partial Gibbs (Helmholtz) energy change per advancement. These relations are developed on the basis of the second law of thermodynamics with reference to entropy production, efficiency and energy dissipation. The symbols of nonequilibrium thermodynamics are not generally in line with IUPAC conventions. Any attempt towards a reconciliation necessarily leads to symbols which are unconventional in either tradition. Importantly, improvement of terminological consistency is a basis for conceptual clarification.

Keywords: List of symbols, Definitions, Nonequilibrium thermodynamics, Open systems, Extensive, Intensive, System-specific Bioblast editor: Gnaiger E O2k-Network Lab: AT Innsbruck Gnaiger E


  • Page 1996, Reference 6: Von Stockar U, Gustafsson L, Larsson C, Marison I, Tissot P, Gnaiger E (1993) Thermodynamic considerations in constructing energy balances for cellular growth. Biochim Biophys Acta 1183:221-40. - »Bioblast link«
  • Page 1997, Table A1, category 7: The unit of conductance is not x2·W-1=x2·J-1·s, but is x2·J-1·s-1.
  • Page 1998, Table A2, category 7': The unit of conductivity (scalar) is not x2·W-1·m-3=x2·J-1·s·m-3, but is x2·J-1·s-1·m-3. Likewise, the unit of conductivity (vector) is not x2·W-1·m-1=x2·J-1·s·m-1, but is x2·J-1·s-1·m-1.
  • Page 1999, Table A3, category 7: The unit of electric conductance is not C2·W-1=C2·J-1·s, but is C2·J-1·s-1.
  • Page 2001, Table A5, category 6: Change of reacting amount of i. This equation in Table A5 has to be replaced by Eq. 2 on page 1984:
drni = dni - deni

Calorimetry and Thermodynamics of Biological Processes

  • International Symposium on Calorimetry and Thermodynamics of Biological Processes, Goteborg-Gullmarsstrand, Sweden, 15–19 May 1992 - »PAC«

Nomenclature update

  • It is suggested to replace the symbol for Gibbs force of reaction, FB,r (Eq. 24), by the symbol ΔrFB.
  • Referred to in Gnaiger 2020 MitoPathways.



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  • Joule [J]; 1 J = 1 N·m = 1 V·C; 1 cal = 4.184 J
Fundamental relationships
» Energy
» Exergy
» Extensive quantity
» Force
» Pressure
» Intensive quantity
Forms of energy
» Internal-energy, dU
» Enthalpy, dH
» Heat, deQ
» Bound energy, dB
Forms of exergy
» Helmholtz energy, dA
» Gibbs energy, dG
» Work, deW
» Dissipated energy, diD


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.::: Fundamental relationships

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» Faraday constant
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HRR: Theory 

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