Statistical Generalization of Regenerative Bosonic and Fermionic Stirling Cycles

TL;DR

This paper develops a unified statistical framework for analyzing bosonic and fermionic Stirling cycles with regenerative features, revealing thermodynamic equivalences in quantum regimes and generalizing heat and work definitions.

Contribution

It introduces a formalism that treats bosonic and fermionic working fluids on equal footing, extending classical thermodynamics to quantum regimes with new definitions and results.

Findings

Thermodynamic equivalence between bosonic and fermionic Stirling cycles in low-temperature regimes.

Derived novel heat transfer rates at low and high temperatures.

Established conditions for equal power, efficiency, and entropy production in quantum Stirling cycles.

Abstract

We have constructed a unified framework for generalizing the finite-time thermodynamic behavior of statistically distinct bosonic and fermionic Stirling cycles with regenerative characteristics. In our formalism, working fluid consisting of particles obeying Fermi-Dirac and Bose-Einstein statistics are treated under equal footing and modelled as a collection of non-interacting harmonic and fermionic oscillators. In terms of frequency and population of the two oscillators, we have provided an interesting generalization for the definitions of heat and work that are valid for classical as well as non-classical working fluids. Based on a generic setting under finite time relaxation dynamics, novel results on low and high temperature heat transfer rates are derived. Characterized by equal power, efficiency, entropy production, cycle time and coefficient of performance, thermodynamic equivalence between two types of Stirling cycles is established in the low temperature "quantum" regime.