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We have constructed an 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.
Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum cellular automa
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new general con
I describe the occurence of Eulerian numbers and Stirling numbers of the second kind in the combinatorics of the Statistical Curse of the Second Half Rank problem.
We consider the application of the original Meyer-Miller (MM) Hamiltonian to mapping fermionic quantum dynamics to classical equations of motion. Non-interacting fermionic and bosonic systems share the same one-body density dynamics when evolving fro
The hierarchical equations of motion (HEOM) method is a powerful numerical approach to solve the dynamics and steady-state of a quantum system coupled to a non-Markovian and non-perturbative environment. Originally developed in the context of physica