  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.
