First passage time and change of entropy

TL;DR

This paper introduces the first-passage time as a new thermodynamic parameter linked to entropy deviation, providing a framework to analyze how external forces influence the timing of stochastic processes.

Contribution

It generalizes the Gibbs distribution by incorporating first-passage time as an independent thermodynamic parameter and relates it to entropy deviation and external forces.

Findings

First passage time is connected to entropy deviation from equilibrium.

The partition function is divided into multipliers related to equilibrium and first-passage parameters.

Changing thermodynamic forces can alter the first passage time.

Abstract

The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first passage statistics itself. A random process is set that describes a physical phenomenon. The first passage statistics is determined from this random process. The thermodynamic parameter conjugated to the first-passage time is the same as the Laplace transform parameter of the first-passage time distribution in the partition function. The corresponding partition function is divided into multipliers, one of which is associated with the equilibrium parameters, and the second one - with the parameters of the first-passage time distribution. The thermodynamic parameter conjugated to the first-passage time can be expressed in terms of the deviation of the entropy from the equilibrium value. Thus, all moments of the distribution of the first passage time are expressed in terms of the deviation of the entropy from its equilibrium value and the external forces acting on the system. By changing the thermodynamic forces, it is possible to change the first passage time.