Quasi-static Decomposition and the Gibbs Factorial in Small Thermodynamic Systems

Sasa, Shin Ichi; Hiura, Ken; Nakagawa, Naoko; Yoshida, Akira

doi:10.1007/s10955-022-02991-7

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…In absence of a formal definition of information, this statement risks to become misleading. Actually, we have shown that the entropy of the occupancy numbers is the complete information about the system because the entropy of microstates belonging to the same macrostate, due to indistinguishability of particles, is not informative, as it is subtracted in (8) to the entropy of microstates.…”

Section: Discussionmentioning

confidence: 99%

Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory

Spalvieri

2023

Preprint

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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.

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Section: Discussionmentioning

confidence: 99%

Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory

Spalvieri

2023

Preprint

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“…In this controversial situation, more than 100 years after its introduction, the Gibbsian log(N!) is still an object of research and debate today; see, e.g., [11][12][13][14][15], see also [16] for the case of small thermodynamic systems.…”

Section: Introductionmentioning

confidence: 99%

Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory

Spalvieri

2024

Entropy

View full text Add to dashboard Cite

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 obtained through two approaches: one involves tracing out the environment from a bosonic eigenstate of the combined environment and system of interest (the empirical approach), while the other involves tracing out the environment from the mixed state of the combined 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.

show abstract

Quasi-static Decomposition and the Gibbs Factorial in Small Thermodynamic Systems

Cited by 2 publications

References 16 publications

Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory

Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory

Entropy of the Canonical Occupancy (Macro) State in the Quantum Measurement Theory

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