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

Michael H. Peters

doi:10.3390/en14082196

Abstract

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.

Highlights

Nonequilibrium entropy conservation for open systems is often the “forgotten” transport equation in the analysis and applications of the conservation laws to physico-chemical systems
Following Irving and Kirkwood’s (IK) paradigm in development of the transport theory for mass, momentum, and energy, the nonequilibrium entropy conservation equation can be obtained by introducing a dynamic variable α, which is defined here in terms of the
Entropy conservation or the Second Law plays a critical role is setting limits on heat and work that are possible in any given system

Summary

Introduction

Nonequilibrium entropy conservation for open systems is often the “forgotten” transport equation in the analysis and applications of the conservation laws to physico-chemical systems. As shown here, Irving and Kirkwood’s methodology can be extended to include entropy conservation and the Second Law. Importantly, as originally shown by Jaynes [2,3], nonequilibrium entropy conservation and the Second Law only follows willful approximations of the underlying molecular probability density functions. As originally shown by Jaynes [2,3], nonequilibrium entropy conservation and the Second Law only follows willful approximations of the underlying molecular probability density functions It is well-known that the Liouville equation itself cannot support the principle of entropy increase and the Second Law without approximations, which we have termed “Liouville’s

Methods

Results

Conclusion