Basic statistical mechanics

Statistical Mechanics of Neocortical Interactions. I. Basic Formulation

An approach to collective aspects of the neocortical system is formulated by methods of modern nonlinear nonequilibrium statistical mechanics. Microscopic neuronal synaptic interactions, consistent with anatomical observations, are first spatially averaged over columnar domains. These spatially ordered domains retain contact with the original physical synaptic parameters, are consistent with ob...

Time-Dependent Statistical Mechanics 1C. The basic postulate of equilibrium statistical mechanics and elementary properties of time correlation functions

Statistical Mechanics

Statistical Mechanics

where pi ≡ p(x = i). If only M of the K states have non-zero probability and that probability is 1/M then S = logM . In this special case the entropy is the log of the number of occupied states. An analog of this special case in the continuous domain occurs in Liouville’s Theorem. This states that if the volume of phase space (i.e. of the x variable, but now multivariate and continuous) is some...

Statistical Inference and Statistical Mechanics

In this lecture, recent developments on connections between Markov processes and nonequilibrium statistical mechanical systems are discussed. A statistical mechanical analogy is developed for Markov processes and a local entropic measure of their true asymmetry is defined. Introducing partial observations, conditional and joint analogies are developed for Markov processes and their optimal filt...