Statistical Mechanics Derived From Quantum Mechanics
Yu-Lei Feng, Yi-Xin Chen
TL;DR
This paper presents a pedagogical derivation of statistical mechanics from quantum mechanics using open quantum systems and introduces a new quantum Boltzmann entropy consistent with superposition, exploring quantum thermodynamics.
Contribution
It provides a novel derivation of statistical mechanics from quantum principles and defines a new quantum Boltzmann entropy based on Hilbert space dimension.
Findings
New quantum Boltzmann entropy is constant and depends only on Hilbert space dimension.
Formal investigation of thermodynamics for quantum systems.
Derivation emphasizes open quantum systems approach.
Abstract
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way consistent with the superposition principle. In particular, this new Boltzmann entropy is a constant that depends only on the dimension of the system's relevant Hilbert subspace. Finally, thermodynamics for quantum systems is investigated formally.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Quantum Mechanics and Applications · Statistical Mechanics and Entropy