What question did this study set out to answer?

To establish a minimal framework that connects various concepts in statistical mechanics to a single principle.

April 19, 2026Open Access

A Minimal Unified Framework: Coarse-Graining Fixed Points and Quantum Statistics

Key Points

To establish a minimal framework that connects various concepts in statistical mechanics to a single principle.
Introduced a framework combining concepts from statistical mechanics, quantum statistics, and renormalization.
Analyzed the mathematical structures common to different statistical models and theorems.
Identified shared principles across Maxwell--Boltzmann, Bose--Einstein, and Fermi--Dirac statistics.
Showed the mathematical similarities between renormalization-group structures and thermodynamic laws.

Abstract

A Minimal Unified Framework: Coarse-Graining Fixed Points and Quantum Statistics Conceptual motivationStatistical mechanics is traditionally formulated as a theory of equilibrium distributions derived from entropy maximization under conservation constraints. However, the same mathematical structure appears in several seemingly distinct contexts: (i) Maxwell--Boltzmann, Bose--Einstein, and Fermi--Dirac statistics, (ii) the central limit theorem (CLT), (iii) renormalization-group (RG) fixed-point structures, and (iv) the thermodynamic zeroth law. This section introduces a minimal framework in which these phenomena are interpreted as manifestations of a single principle

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Cite This Study

Makoto Izumi (Fri,) studied this question.

synapsesocial.com/papers/69e472d8010ef96374d8ecf0 https://doi.org/https://doi.org/10.5281/zenodo.19631898

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