Influence of Entropy Changes on First Passage Time in the Thermodynamics of trajectories

TL;DR

This paper investigates how entropy changes influence the first passage time in trajectory thermodynamics, revealing relationships in both classical and quantum systems and emphasizing the role of entropy in nonequilibrium and equilibrium states.

Contribution

It establishes a quantitative relationship between entropy change and first passage time, extending the thermodynamics of trajectories to include dynamic activity and quantum systems.

Findings

FPT correlates with total entropy change in various systems.

Dependencies on entropy are observed in stationary nonequilibrium and equilibrium states.

Models show how entropy influences FPT in classical and quantum two- and three-level systems.

Abstract

An ensemble of trajectories with dynamical activity and first-passage time (FPT) is considered in the context of the thermodynamics of trajectories. The relationship between the average FPT and the total change in entropy is determined, with a focus on non-negative values of the total change in entropy only. Similar dependencies were found for dynamic activity, the dispersion of dynamic activity, and FPT, as well as for the correlation between dynamic activity and FPT. Applying the obtained results to model systems reveals dependencies on entropy changes in stationary nonequilibrium and equilibrium states. To relate changes in entropy to the conjugate parameter of the FPT, three models of the distribution function are applied to classical two- and three-level systems, and to a quantum two-level system.