2023/07/11 by Paula Reichert, Reichert, Paula · 1 citation
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical Physics (physics.class-ph) #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Mathematical Physics (math-ph) #Phase Equilibria and Thermodynamics #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2307.05166
openalex publication_date 2023/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper analyzes the ergodic hypothesis in the context of Boltzmann's late work in statistical mechanics, where Boltzmann lays the foundations for what is today known as the typicality account. I argue that, based on the concepts of stationarity (of the measure) and typicality (of the equilibrium state), the ergodic hypothesis, as an idealization, is a consequence rather than an assumption of Boltzmann's approach. More precisely, it can be shown that every system with a stationary measure and an equilibrium state (be it a state of overwhelming phase space or time average) behaves essentially as if it were ergodic. I claim that Boltzmann was aware of this fact as it grounds both his notion of equilibrium, relating it to the thermodynamic notion of equilibrium, and his estimate of the fluctuation rates.