2023/03/16 by Ignacio E. Tapia, Tapia, Ignacio, Gonzalo Gutiérrez +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2303.09672
openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical mechanical models from a variational principle, provided that the adequate time-dependent constraints and the state of the system at some specific times are given. The approach is exemplified by obtaining the description of a time-dependent Brownian particle from kinetic restrictions. We relate the predictive nature of a model to the structure of the prior distribution that represents the state of knowledge about the system before the dynamical constraints are considered. Non-predictive models are shown to be possible in the presented framework and as an example, retrodictive dynamics are obtained from the same kinetic constraints.