This study employed entropy-based second law post-processing analysis to characterize the various thermodynamic losses inside a 3-space solution domain (gas spring + heat exchanger + regenerator) operating under conditions of oscillating pressure and oscillating flow. The 3-space solution domain is adapted from the 2-space solution domain (gas spring + heat exchanger) in Kornhauser's MIT test rig by modifying the heat exchanger space to include a porous regenerator system. A thermal non-equilibrium model which assumes that the regenerator porous matrix and gas average temperatures can differ by several degrees at a given axial location and time during the cycle is employed. An important and primary objective of this study is the development and application of a thermodynamic loss post-processor to characterize the major thermodynamic losses inside the 3-space model. It is anticipated that the experience gained from thermodynamic loss analysis of the simple 3-space model can be extrapolated to more complex systems like the Stirling engine. It is hoped that successful development of loss post-processors will facilitate the improvement of the optimization capability of Stirling engine analysis codes through better understanding of the heat transfer and power losses. It is also anticipated that the incorporation of a successful thermal nonequilibrium model of the regenerator in Stirling engine CFD analysis codes, will improve our ability to accurately model Stirling regenerators relative to current multi-dimensional thermal-equilibrium porousmedia models.