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 fluids consisting of particles obeying Fermi-Dirac and Bose-Einstein statistics are treated on equal footing and modeled as a collection of noninteracting harmonic and fermionic oscillators. In terms of the 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 nonclassical working fluids. Based on a generic setting under finite-time relaxation dynamics, nice results on low- and high-temperature heat transfer rates are derived. Characterized by equal power, efficiency, entropy production, cycle time, and coefficient of performance, the thermodynamic equivalence between two types of Stirling cycles is established in the low-temperature "quantum" regime.
