  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.
