Comparison of extended irreversible thermodynamics and nonequilibrium statistical operator method with thermodynamics based on a distribution containing the first-passage time

TL;DR

This paper compares extended irreversible thermodynamics and the nonequilibrium statistical operator method, introducing a distribution with a first-passage time parameter, and explores their equivalence and implications for thermodynamic modeling.

Contribution

It establishes a mapping between thermodynamics with a first-passage time parameter and extended irreversible thermodynamics, providing new expressions for thermodynamic parameters and average first-passage times.

Findings

Thermodynamics with first-passage time maps to extended irreversible thermodynamics.

Expressions derived for conjugate thermodynamic parameters and average first-passage times.

Replaces relaxation time with average first-passage time in thermodynamic models.

Abstract

An analogy is drawn between version of non-equilibrium thermodynamics a distribution-based containing an additional thermodynamic first-passage time parameter, nonequilibrium statistical operator method and extended irreversible thermodynamics with flows as an additional thermodynamic parameter. Thermodynamics containing an additional thermodynamic first-passage time parameter maps to extended irreversible thermodynamics. Various conditions for the dependence of the distribution parameters of the first-passage time on the random value of energy, the first thermodynamic parameter, are considered. Time parameter relaxation time {\tau} of extended irreversible thermodynamics is replaced by the average first-passage time. Expressions are obtained for the thermodynamic parameter, the conjugate of the first passage time through the entropy change, and for the average first passage time through the flows.