Effects of the kinetic energy in heat for overdamped systems

TL;DR

This paper demonstrates that including kinetic energy in the thermodynamics of overdamped systems is essential for accurate heat distribution calculations, bridging the gap between underdamped and overdamped descriptions.

Contribution

It reveals the necessity of considering kinetic energy in overdamped thermodynamics, which was previously often neglected, through detailed analysis of multiple systems.

Findings

Kinetic energy significantly affects heat distribution in overdamped systems.

Neglecting kinetic energy leads to discrepancies between underdamped and overdamped thermodynamics.

The study applies to harmonic, logarithmic, and non-isothermal processes.

Abstract

In the derivation of the thermodynamics of overdamped systems, one ignores the kinetic energy contribution, since the velocity is a slow variable. In this paper, we show that the kinetic energy needs to be present in the calculation of the heat distribution to have a correct correspondence between the underdamped and overdamped cases, meaning that the velocity can not be fully ignored in the thermodynamics of these systems. We do this by investigating in detail the effect of the kinetic energy for three different systems, the harmonic potential, the logarithm potential, and an arbitrary non-isothermal process.