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The European Physical Journal Plus

Irreversibility and entropy production in two coupled bosonic modes interacting with a thermal environment

Tatiana Mihaescu, Аурелиан Исар

Published Jan 22, 2024• 3 citations
Publisher
DOI
10.1140/epjp/s13360-024-04869-x

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Quantum Decay in Coupled Bosonic Systems

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The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system.
As stated by the second law of thermodynamics, the irreversible entropy of a system keeps being produced until it reaches the equilibrium, and the entropy production rate is always non-negative. But when some exotic quantum properties, e.g., quantum coherence or squeezing, exist in the bath, it has been reported that the 2nd law does not apply. Correspondingly, the previous description of the entropy production rate does not apply either, and it is not always non-negative in these cases. We notice that the entropy production rate can be generalized to be the increasing rate of the mutual information between the open system and its environment. For thermal baths, this mutual information production rate equals to the previous entropy production rate. For non-thermal baths, in an example of a single boson mode interacting with multiple squeezed thermal baths, we proved that the mutual information production rate is always non-negative. The monotonic increasing mutual information means the system and its environment are becoming more and more correlated during the evolution.
When an open system comes into contact with several thermal baths, the entropy produced by the irreversible processes (dS_{i}=dS-∑_{α} đQ_{α}/T_{α}) keeps increasing, and this entropy production rate is always non-negative. However, when the system comes into contact with nonthermal baths containing quantum coherence or squeezing, this entropy production formula does not apply. In this paper, we study the increasing rate of mutual information between an open system and its environment. In the case of canonical thermal baths, we prove that this mutual information production rate could return exactly to the previous entropy production rate. Furthermore, we study an example of a single boson mode that comes into contact with multiple squeezed thermal baths, where the conventional entropy production rate does not apply, and we find that this mutual information production rate remains non-negative, which indicates a monotonic increase in the correlation between the system and its environment.