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Axioms for the Boltzmann Distribution.

Adam Brandenburger1, Kai Steverson2

  • 11Stern School of Business, Tandon School of Engineering, NYU Shanghai, New York University, 44 West 4th Street, New York, NY 10012 USA.

Foundations of Physics
|June 1, 2019
PubMed
Summary
This summary is machine-generated.

This study derives the Boltzmann distribution in statistical mechanics without assuming equal microstate probabilities. It uses two new axioms: thermal equilibrium and unrestricted energy exchange, providing a clearer physical foundation.

Keywords:
AxiomsBoltzmann distributionEqual-probability postulateThermodynamics

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Area of Science:

  • Statistical Mechanics
  • Foundations of Physics

Background:

  • The equal probability postulate for microstates in isolated systems is a cornerstone of statistical mechanics.
  • This postulate, attributed to Boltzmann, lacks a clear physical basis and has faced criticism.

Purpose of the Study:

  • To derive the canonical (Boltzmann) distribution without relying on the equal probability postulate.
  • To establish a more physically grounded foundation for the Boltzmann distribution.

Main Methods:

  • Introduction of two new axioms with distinct physical interpretations.
  • Axiom 1: Thermal Equilibrium - Ensures consistent probability rankings of system states when interacting with different heat baths, preventing population inversions.
  • Axiom 2: Energy Exchange - Guarantees that any probability distribution can be achieved through unrestricted energy flow between a system and its heat bath.

Main Results:

  • The two proposed axioms uniquely identify the Boltzmann distribution.
  • Demonstration that the axioms provide a robust derivation of the canonical distribution.

Conclusions:

  • The canonical (Boltzmann) distribution can be derived from fundamental physical axioms without the controversial equal probability postulate.
  • The proposed axioms offer a clearer physical interpretation and foundation for statistical mechanics.
  • This work refines our understanding of thermal equilibrium and energy exchange in physical systems.