Asymmetric temperature equilibration with heat flow from cold to hot in a quantum thermodynamic system

TL;DR

This paper demonstrates that in a quantum thermodynamic system with asymmetric coupling, heat can flow from cold to hot, and a quantum entropy measure continues to increase, supporting a second law-like behavior.

Contribution

It introduces a quantum thermodynamic model showing heat flow from cold to hot and validates a quantum entropy measure that upholds the second law in asymmetric conditions.

Findings

Quantum baths reach asymmetric equilibrium with different energies and temperatures.

Quantum entropy $S^Q_{univ}$ increases monotonically, aligning with the second law.

Von Neumann entropy fails to uphold the entropy law in this scenario.

Abstract

A model computational quantum thermodynamic network is constructed with two variable temperature baths coupled by a linker system, with an asymmetry in the coupling of the linker to the two baths. It is found in computational simulations that the baths come to "thermal equilibrium" at different bath energies and temperatures. In a sense, heat is observed to flow from cold to hot. A description is given in which a recently defined quantum entropy $S^Q_{univ}$ for a pure state "universe" continues to increase after passing through the classical equilibrium point of equal temperatures, reaching a maximum at the asymmetric equilibrium. Thus, a second law account $\Delta S^Q_{univ} \ge 0$ holds for the asymmetric quantum process. In contrast, a von Neumann entropy description fails to uphold the entropy law, with a maximum near when the two temperatures are equal, then a decrease $\Delta S^{vN} < 0$ on the way to the asymmetric equilibrium.