The Definition of Entropy for Quantum Unstable Systems: A View-Point Based on the Properties of Gamow States

TL;DR

This paper extends the concept of entropy to quantum unstable systems by incorporating complex-energy states and resonances, resulting in a generalized entropy with real and imaginary parts, and explores its physical interpretation.

Contribution

It introduces a generalized entropy definition for quantum unstable systems that includes complex-energy states and resonances, expanding traditional thermodynamic concepts.

Findings

Derived an entropy expression with real and imaginary components.

Linked the imaginary part of entropy to thermal and time evolution.

Provided a framework for understanding entropy in unstable quantum systems.

Abstract

In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy states. After introducing a generalized basis of states which includes resonances, and working with amplitudes instead of probabilities, we~found an expression for the entropy which exhibits real and imaginary components. We discuss the meaning of the imaginary part of the entropy on the basis of the similarities existing between thermal and time evolutions.