Entropy exchange and thermal fluctuations in the Jaynes-Cummings model

TL;DR

This paper investigates how thermal fluctuations and entropy exchange affect a two-level atom interacting with a cavity mode within the Jaynes-Cummings model, using superstatistics and non-additive entropy formalisms.

Contribution

It introduces a superstatistics approach with gamma and multi-level distributions to analyze entropy dynamics under temperature fluctuations in the Jaynes-Cummings model.

Findings

The $q$-parameter significantly influences entropy in the gamma distribution case.

Inverse temperature distribution impacts entropy functions.

Thermal fluctuations modify the entropy exchange in the system.

Abstract

The time-dependence of the quantum entropy for a two-level atom interacting with a single-cavity mode is computed using the Jaynes-Cummings model, when the initial state of the radiation field is prepared in a thermal state with temperature fluctuations. In order to describe the out-of-equilibrium situation, the Super Statistics approximation is implemented so that the gamma and the multi-level distribution functions are used to introduce the inverse temperature fluctuations. In the case of the gamma distribution, paralleling the Tsallis non-additive formalism, the entropy for the system is computed with the $q$-logarithm prescription, and the impact of the initial state of the atom is also taken into account. The results show that, in the first distribution, the $q$-parameter (related to the thermal fluctuations) modifies the partial entropies appreciably. In contrast, the way the inverse temperatures are distributed in the second one may lead to changes in the entropy functions.