https://doi.org/10.1140/epjp/s13360-024-05492-6
Regular Article
Quantum thermodynamics in the random matrix approach: a study of 
-three-level atom coupled to two heat baths
Department of Physics, University of Garmian, Kalar, KRG, Iraq
a amoradian@garmian.edu.krd, moradianadam@gmail.com
Received:
12
December
2023
Accepted:
24
July
2024
Published online:
4
August
2024
This paper delves into the thermodynamics of a -three-level atom interacting with two quantum external electromagnetic fields at both equal and unequal temperatures within a left-sided Markovian matrix framework. In resonance, the total Hamiltonian is dissected into matrices with computations for eigenvalues, eigenvectors, and density matrix evolution. Averaging over extended times yields stable, time-independent quantities, excluding transitional, and fast oscillating evolution. Heat baths at different temperatures interact with a three-level atom which model as the left-sided Markovian matrix. The study computes the distribution function of heat and entropy, their averages, and heat conductivity. Near the equilibrium point, both the entropy increase, 
, and the absorbed heat over temperature, 
, exhibit a common tangent. This indicates that the heat conductivity is positive. The traditional Clausius statement is replaced by two inequalities highlighting the positive heat conductivity coefficient. The scaled averages of heat and entropy exerted on the system are illustrated and discussed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
