Comparison of Thermodynamic Characteristics in Ordinary Quantum and Classical Approaches and Game Theory

TL;DR

This paper compares quantum and classical thermodynamic characteristics by modeling mean energy and entropy as players in a game, deriving formulas, and establishing inequalities without assuming small Planck's constant.

Contribution

It introduces a game-theoretic framework to compare quantum and classical thermodynamics, deriving new formulas and inequalities without small Planck's constant assumptions.

Findings

Derived formulas for quantum and classical mean energy and entropy.

Established inequalities relating statistical sum, energy, and entropy.

Compared quantum and classical approaches without small Planck's constant assumption.

Abstract

We fix the temperature $T$ and consider mean energy and Boltzmann-Gibbs-Shannon entropy as two players of a game. As a result, basic formulas for the ordinary quantum mean energy and the Boltzmann-Gibbs-Shannon entropy are derived. We compare also the quantum and classical approaches without a demand for Plank's constant being small. Important inequalities for statistical sum, quantum energy, quantum entropy, and their classical analogs follow.