Effective temperatures for single particle system under dichotomous noise

TL;DR

This paper compares three definitions of effective temperature in a non-equilibrium Langevin system driven by dichotomous noise, analyzing their differences and convergence as the noise approaches Gaussian behavior.

Contribution

It systematically evaluates and compares three distinct effective temperature definitions within a non-equilibrium Langevin framework under dichotomous noise, highlighting their convergence in the white-noise limit.

Findings

Differences between effective temperature definitions diminish as noise approaches Gaussian characteristics.

In the overdamped limit, all three effective temperature definitions become equivalent.

The framework bridges kinetic, entropy, and response-based temperature concepts in non-equilibrium systems.

Abstract

Three different definitions of effective temperature -- $\mathcal{T}_{\rm k}$, $\mathcal{T}_{\rm i}$ and $\mathcal{T}_{\rm r}$ related to kinetic theory, system entropy and response theory, respectively -- are applied in the description of a non-equilibrium generalised massive Langevin model in contact with dichotomous noise. The differences between the definitions of $\mathcal{T}$ naturally wade out as the reservoir reaches its white-noise limit, approaching Gaussian features. The same framework is employed in its overdamped version as well, showing the loss of inertial contributions to the dynamics of the system also makes the three mentioned approaches for effective temperature equivalent.