Time-dependent Nonequilibrium Thermodynamics: A Master-equation Approach

TL;DR

This paper develops a rigorous, time-dependent nonequilibrium thermodynamics framework for master equations, introducing a generalized internal energy and extended equilibrium states, and confirms its consistency with classical thermodynamics.

Contribution

It provides a novel theoretical framework for nonequilibrium thermodynamics of biochemical systems using master equations, including new definitions and an extended Second Law.

Findings

Derived a general theory for time-dependent nonequilibrium thermodynamics

Introduced a concept of generalized internal energy and extended equilibrium states

Established an explicit form of the extended Second Law

Abstract

Master equation could be applied to model various kinds of biochemical systems. A general theory for its time-dependent nonequilibrium thermodynamics is rigorously derived. We not only introduce a concept of general internal energy, but also propose an extension of the equilibrium state. Moreover, we find out an explicit expression for the extended form of the Second Law, which is phenomenologically stated as "the conversion of work to excess heat is irreversible". The theory is carefully applied to several thermodynamic processes, and its consistence with the classical thermodynamics is clearly shown.