Two simple models of classical heat pumps

Motivated by recent studies of 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.

Figure 1

(Color online) Plot of ${\dot{q}}_L$, ${\dot{q}}_R$, and $\dot{w}$ versus $\varphi$ with both baths at the same temperature. The inset shows the currents for the case where the right bath is slightly colder.

Figure 2

(Color online) Plot of ${\dot{q}}_L$, ${\dot{q}}_R$, and $\dot{w}$ versus $\varphi$ for parameter values chosen such that the model performs as an engine.

Figure 3

(Color online) Plot of ${\dot{Q}}_L$, ${\dot{Q}}_R$, and $\dot{W}$ as a function of time for parameters corresponding to pump and engine (inset).

Figure 4

(Color online) Plots of heat transfer and work done as a function of phase difference $\varphi$ in the two-particle model. Here $\Omega =2\pi ∕3$.