The entropy concept for non-equilibrium states

TL;DR

This paper explores the challenges of defining a unique entropy for non-equilibrium states, proposing two entropy functions that characterize possible adiabatic processes between such states.

Contribution

It introduces the concept of two entropy functions, S_- and S_+, for non-equilibrium states, extending the classical entropy framework.

Findings

Unique entropy cannot generally be defined for non-equilibrium states

Two entropy functions, S_- and S_+, characterize adiabatic process ranges

Comparability of states is crucial for understanding non-equilibrium entropy

Abstract

In earlier work we presented a foundation for the Second Law of Classical Thermodynamics in terms of the Entropy Principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties and whose increase is a necessary and sufficient condition for an adiabatic process between two states to be possible. Here, after a brief review of this approach, we address the question of defining entropy for non-equilibrium states. Our conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties. We do show, however, that one can define two entropy functions, called $S_-$ and $S_+$, which, taken together, characterize the range of adiabatic processes that can occur between non-equilibrium states. The concept of {\it comparability} of states with respect to adiabatic changes plays an important role in our reasoning.