Two simple models of classical heat pumps

TL;DR

This paper investigates two simple classical models of heat pumps, demonstrating that one can function as a heat pump while the other cannot, despite their similar principles.

Contribution

It introduces and analyzes two minimal classical models of heat pumps, providing exact solutions and clarifying conditions for heat pumping functionality.

Findings

One model functions as a heat pump, the other does not.

Both models are analytically solvable and interpretable.

The study clarifies principles underlying classical heat pumping.

Abstract

Motivated by recent studies on models of particle and heat quantum pumps, we study similar simple classical models and examine the possibility of heat pumping. Unlike many of the usual ratchet models of molecular engines, the models we study do not have particle transport. We consider a two-spin system and a coupled oscillator system which exchange heat with multiple heat reservoirs and which are acted upon by periodic forces. The simplicity of our models allows accurate numerical and exact solutions and unambiguous interpretation of results. We demonstrate that while both our models seem to be built on similar principles, one is able to function as a heat pump (or engine) while the other is not.