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Nonequilibrium Entropy Conservation and the Transport Equations of Mass, Momentum, and Energy


  • Michael H. Peters

    (Department of Chemical and Life Science Engineering, Virginia Commonwealth University, 601 West Main St., Richmond, VA 23284, USA)


Nonequilibrium statistical mechanics or molecular theory has put the transport equations of mass, momentum and energy on a firm or rigorous theoretical foundation that has played a critical role in their use and applications. Here, it is shown that those methods can be extended to nonequilibrium entropy conservation. As already known, the “closure” of the transport equations leads to the theory underlying the phenomenological laws, including Fick’s Law of Diffusion, Newton’s Law of Viscosity, and Fourier’s Law of Heat. In the case of entropy, closure leads to the relationship of entropy flux to heat as well as the Second Law or the necessity of positive entropy generation. It is further demonstrated how the complete set of transport equations, including entropy, can be simplified under physically restrictive assumptions, such as reversible flows and local equilibrium flows. This analysis, in general, yields a complete, rigorous set of transport equations for use in applications. Finally, it is also shown how this basis set of transport equations can be transformed to a new set of nonequilibrium thermodynamic functions, such as the nonequilibrium Gibbs’ transport equation derived here, which may have additional practical utility.

Suggested Citation

  • Michael H. Peters, 2021. "Nonequilibrium Entropy Conservation and the Transport Equations of Mass, Momentum, and Energy," Energies, MDPI, vol. 14(8), pages 1-8, April.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:8:p:2196-:d:536228

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    Cited by:

    1. Igor Donskoy, 2022. "On the Existence and Applicability of Extremal Principles in the Theory of Irreversible Processes: A Critical Review," Energies, MDPI, vol. 15(19), pages 1-23, September.


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