Steepest entropy ascent paths towards the MaxEnt distribution
Abstract
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 squareroot 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 nonequilibrium 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 nonequilibrium affinity.
 Publication:

arXiv eprints
 Pub Date:
 December 2013
 arXiv:
 arXiv:1312.5043
 Bibcode:
 2013arXiv1312.5043B
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 6 pages, 2 figures, presented at the MaxEnt2013 conference in Canberra, Australia, December 1520, 2013