2013/12/18 by Gian Paolo Beretta, Beretta, Gian Paolo
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #Data Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Statistics and Probability (physics.data-an) #cond-mat.stat-mech #math-ph #math.MP #physics.data-an
paper · pdf · doi:10.48550/arxiv.1312.5043
6 pages, 2 figures, presented at the MaxEnt2013 conference in Canberra, Australia, December 15-20, 2013
arxiv created 2013/12/18 · openalex publication_date 2013/12/18 · arxiv updated 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With reference to two general probabilistic description frameworks, Information Theory and Classical Statistical Mechanics, we discuss the geometrical reasoning and mathematical formalism leading to the differential equation that defines in probability space the smooth path of Steepest Entropy Ascent (SEA) connecting an arbitrary initial probability distribution to the unique Maximum Entropy (MaxEnt) distribution with the same mean values of a set of constraints. The SEA path is relative to a metric chosen to measure distances in square-root probability distribution space. Along the resulting SAE path, the metric turns out to be proportional to the concept of Onsager resistivity generalized to the far non-equilibrium domain. The length of the SEA path to MaxEnt provides a novel global measure of degree of disequilibrium (DoD) of the initial probability distribution, whereas a local measure of DoD is given by the norm of a novel generalized concept of non-equilibrium affinity.