On the microscopic basis of Newton's law of cooling and beyond

TL;DR

This paper explores the microscopic foundations of Newton's law of cooling, highlighting how bath dynamics influence cooling rates and proposing a generalized model that accounts for early-time deviations from classical predictions.

Contribution

It introduces a microscopic framework that incorporates bath dynamics and feedback effects, extending Newton's law of cooling beyond traditional assumptions.

Findings

Early-time cooling is faster than classical predictions.

Bath dynamics significantly affect the cooling process.

The model generalizes the Born-Markov master equation for small baths.

Abstract

The microscopic basis of Newton's law of cooling and its modification when the difference in temperature between the system and the surroundings is very large is discussed. When the system of interest is interacting with a small bath, the effect of the dynamical evolution of the bath variables is important to find out its dynamical feedback on the system. As in the usual system-bath approach, however, the bath is finally considered to be in thermal equilibrium and thereby provides an effective generalization of the Born-Markov master equation. It is shown that the cooling at early time is faster than that predicted by Newton's law due to the dynamical feedback of the bath.