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Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory
Version 1
: Received: 14 December 2023 / Approved: 18 December 2023 / Online: 18 December 2023 (10:18:41 CET)
A peer-reviewed article of this Preprint also exists.
Spalvieri, A. Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory. Entropy 2024, 26, 107. Spalvieri, A. Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory. Entropy 2024, 26, 107.
Abstract
The paper analyzes the probability distribution of the occupancy
numbers and the entropy of a system at the equilibrium composed by
an arbitrary number of non-interacting bosons. The probability
distribution is derived both by tracing out the environment from a
bosonic eigenstate of the union of environment and system of
interest (the empirical approach) and by tracing out the
environment from the mixed state of the union of environment and
system of interest (the Bayesian approach). In the thermodynamic
limit, the two coincide and are equal to the multinomial
distribution. Furthermore, the paper proposes to identify the
physical entropy of the bosonic system with the Shannon entropy of
the occupancy numbers, fixing certain contradictions that arise in
the classical analysis of thermodynamic entropy. Finally, by
leveraging an information-theoretic inequality between the entropy
of the multinomial distribution and the entropy of the
multivariate hypergeometric distribution, Bayesianism of
information theory and empiricism of statistical mechanics are
integrated into a common ''infomechanical'' framework.
Keywords
Occupancy Numbers; Multivariate Hypergeometric Distribution; Multinomial Distribution; Canonical Typicality; Gibbs Correction Factor; Sackur-Tetrode Entropy Formula
Subject
Physical Sciences, Thermodynamics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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