The Heat Distribution of the Underdamped Langevin Equation

TL;DR

This paper derives exact, general solutions for the heat distribution in the underdamped Langevin equation across multiple potentials and dimensions, extending previous overdamped and one-dimensional results.

Contribution

It provides the first comprehensive, exact solutions for heat distribution in the underdamped regime for various potentials and dimensions, broadening the scope of stochastic thermodynamics.

Findings

Exact heat distribution solutions for free particle, linear, and harmonic potentials.

Generalizes known overdamped results to underdamped, multi-dimensional cases.

Extends stochastic thermodynamics understanding in complex regimes.

Abstract

In Stochastic Thermodynamics, heat is a random variable with a probability distribution associated. Studies of the distribution of heat are mostly in the overdamped regime and in one dimension. Here we solve the heat distribution in the underdamped regime for three different cases: the free particle, the linear potential, and the harmonic potential. All of them in arbitrary dimensions. The results are exact and generalize known results in the literature.