Thermodynamic Cost of Regeneration in a Quantum Stirling Cycle

TL;DR

This paper analyzes the thermodynamic cost of regeneration in a quantum Stirling cycle, showing that including regeneration costs prevents super-Carnot efficiencies and ensures thermodynamic consistency.

Contribution

It introduces a framework to account for regeneration costs in quantum Stirling cycles, modifying efficiency bounds and providing rigorous thermodynamic limits.

Findings

Regeneration process incurs a non-zero work cost, affecting cycle efficiency.

Including regeneration costs removes super-Carnot efficiencies, aligning with thermodynamic laws.

Derived bounds ensure the cycle's thermodynamic consistency with quantum relative entropy.

Abstract

We study the standard four-stroke regenerative quantum Stirling heat engine cycle, which assumes local thermal equilibrium at each stage, within the standard weak-coupling, Markovian open quantum system framework. We point out that the regeneration process is not thermodynamically free in a reduced open-system description, and we treat the required work input as an explicit regeneration cost by modifying the cycle efficiency accordingly. We consider two working substances--a single spin-$1/2$ and a pair of interacting spin-$1/2$ particles--and investigate the cycle performance by taking the regeneration cost at its minimum value set by the Carnot heat-pump limit. For comparison, we also analyze the conventional Stirling cycle without regeneration under the same conditions. The super-Carnot efficiencies reported under the cost-free regeneration assumption disappear once the regeneration cost is included: the modified efficiency stays below the Carnot bound, while still remaining higher than the efficiency of the conventional Stirling cycle. For the conventional Stirling cycle, we provide a rigorous Carnot bound using quantum relative entropy, whereas for the regenerative cycle we derive a sufficient lower bound on the regeneration cost that guarantees thermodynamic consistency. Finally, we suggest three candidate quantum regenerator models for future work.