Anomalous law of cooling

TL;DR

This paper investigates the cooling behavior of systems in contact with a thermal reservoir, revealing anomalous oscillations in temperature decay due to non-Markovian effects, while confirming the second law of thermodynamics.

Contribution

It introduces a generalized Langevin framework to describe non-Markovian cooling, showing how memory effects lead to anomalous temperature oscillations.

Findings

Temperature decay can oscillate due to memory effects.

Entropy always increases, complying with thermodynamics.

Relaxation time depends on velocity autocorrelation.

Abstract

We analyze the temperature relaxation phenomena of systems in contact with a thermal reservoir that undergo a non-Markovian diffusion process. From a generalized Langevin equation, we show that the temperature is governed by a law of cooling of the Newton's law type in which the relaxation time depends on the velocity autocorrelation and is then characterized by the memory function. The analysis of the temperature decay reveals the existence of an anomalous cooling in which the temperature may oscillate. Despite this anomalous behavior, we show that the variation of entropy remains always positive in accordance with the second law of thermodynamics.