Entropy of the Canonical Occupancy (Macro) State in the Quantum
Measurement Theory
- URL: http://arxiv.org/abs/2308.04472v6
- Date: Fri, 29 Dec 2023 08:12:10 GMT
- Title: Entropy of the Canonical Occupancy (Macro) State in the Quantum
Measurement Theory
- Authors: Arnaldo Spalvieri
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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 and empiricism are integrated into a common ''infomechanical''
framework.
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