Classical emulation of quantum-coherent thermal machines

TL;DR

This paper demonstrates that quantum coherence in thermal machines can be emulated classically, showing that coherence is not always essential for their thermodynamic performance, through comparison of quantum models and classical graph-based representations.

Contribution

It provides a classical graph-theoretic framework to emulate quantum thermal machines, challenging the notion that quantum coherence is necessary for their enhanced performance.

Findings

Four-level model outperforms three-level in certain regimes

Cooling rate improvement matches quantum coherence increase

Classical models can replicate steady-state thermodynamics of quantum machines

Abstract

The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But, is this connection always an evidence of `quantum-thermodynamic supremacy'? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot, it may exhibit a larger cooling rate, and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any N-level weakly driven device with a `cyclic' pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process.