On Studies of Entropy of Classical and Quantum Kac Rings

TL;DR

This paper explores the quantum analog of Kac rings, analyzing entropy, recurrence, and time distribution, and compares these quantum features to classical Kac rings to deepen understanding of statistical physics concepts.

Contribution

It introduces a quantum version of the Kac ring model and studies its entropy and recurrence properties, highlighting differences from the classical model.

Findings

Quantum Kac rings show different recurrence times compared to classical ones.

Entropy evolution in quantum Kac rings exhibits unique time distribution patterns.

Comparison reveals insights into quantum effects on thermodynamic quantities.

Abstract

Statistical physics is important in understanding the physics of interacting many bodies. This has been historically developed by attempts to understand colliding gases and quantifying quantities like entropy, free energy, and other thermodynamic quantities. An important contribution in statistical physics was by Boltzmann in the form of the H-theorem, which considered collisions between particles and used the assumption of molecular chaos or Stosszahlansatz to understand macroscopic irreversibility. To elucidate these ideas, Mark Kac introduced a classical analog called Kac rings. In this work, we attempt to introduce quantum-ness in a Kac ring and study its entropy and recurrence, comparing and contrasting to corresponding trends in a classical Kac ring. We look at the trends of recurrence time for a system with a qubit as a pointer. We further study the time distribution of entropy for these systems.