Investigation of Quantum Lenoir Engine Efficiency of Non-relativistic and Relativistic Quantum Systems in Pure- and Mixed-state Formalisms

Abstract

In this study, we consider a two-state single particle confined in a one-dimensional box system undergoing a Lenoir cycle. The quantum system is represented as a set of canonical ensembles, and thus the mixed-state probability distribution of the particle is described by the Maxwell-Boltzmann distribution. We calculate the efficiency formulations for relativistic and non-relativistic working substances and analyze the associated physical parameters therein. We also compare the results with those obtained from a quantum Lenoir engine using a pure-state working substance and classical working substances. We found that the non-relativistic working substance has a higher efficiency than the relativistic and classical working substances at the same compression ratio. The higher compression ratio increases efficiency among all types of working substances studied. Furthermore, a quantum Lenoir engine using a mixed-state working substance has the same efficiency formulation as that of the pure-state working substance, but with a limited compression ratio. The efficiency of the mixed-state working substance depends on two physical parameters, viz., the reservoir temperature ratio and the initial box width, regardless of the initial temperature. While a very high temperature ratio can enhance this efficiency, it remains lower than that of the pure-state working substance for the same two-state quantum system.