Heat fluctuations in the logarithm-harmonic potential

TL;DR

This paper analytically and numerically investigates the statistical properties of heat exchange in a Brownian particle within a logarithm-harmonic potential, providing a comprehensive characterization of its distribution and asymptotic behavior.

Contribution

It derives the characteristic function and moments of the heat, and computes the full probability distribution using numerical methods, advancing understanding of heat fluctuations in such potentials.

Findings

Analytical expressions for the characteristic function and moments.

Numerical calculation of the heat distribution.

Asymptotic analysis involving hypergeometric functions.

Abstract

Thermodynamic quantities, like heat, entropy, or work, are random variables, in stochastic systems. Here, we investigate the statistics of the heat exchanged by a Brownian particle subjected to a logarithm-harmonic potential. We derive analytically the characteristic function and its moments for the heat. Through numerical integration, and numerical simulation, we calculate the probability distribution as well, characterizing fully the statistical behavior of the heat. The results are also investigated in the asymptotic limit, where we encounter the characteristic function in terms of hypergeometric functions.