Statistical Entropy of Open Quantum Systems

TL;DR

This paper explores the application of the Maximum Entropy Formalism to dissipative quantum systems, revealing challenges in defining consistent thermodynamics due to non-extensivity and showing that common entropy forms can lead to incorrect results.

Contribution

It introduces a novel approach to modeling dissipative quantum systems using the Maximum Entropy Formalism and highlights limitations of existing entropy measures in this context.

Findings

Non-extensive nature of dissipative quantum systems.

Common entropy forms may produce incorrect thermodynamic predictions.

Counterexample demonstrating limitations of current entropy approaches.

Abstract

Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic properties with those of the well - established approaches. Due to the non-negligible coupling to the heat reservoir, these systems are non-extensive by nature, and the former task may require the use of non-extensive parameter dependent informational entropies. In doing so, we address the problem of choosing appropriate forms of those entropies in order to describe a consistent thermodynamics for dissipative quantum systems. Nevertheless, even having chosen the most successful and popular forms of those entropies, we have proven our model to be a counterexample where this sort of approach leads us to wrong results.