2023/10/06 by Jun Yan Lau, Lau, Jun Yan
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Astrophysics of Galaxies (astro-ph.GA) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Plasma Physics (physics.plasm-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2310.04508
openalex publication_date 2023/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in both Boltzmann's paradigm and Gibbs' paradigm. A rigorous definition of the macrostate enables application of this statistical mechanical theory to self-gravitating systems, by decoupling time-averages and ensemble averages. I compute two-point correlation functions for self-gravitating and electrostatic systems.