Foundations and History of Statistical Mechanics

22 Jul 2022 11:29

Technical issues: things like, what exactly is a C* algebra? Role of large deviations.

Conceptual issues: Why is it legitimate to treat deterministic mechanical systems with many unstable degrees of freedom as stochastic processes? (My impulse is to appeal to ergodic theory.) When and why do we get convergence to equilibria characterized by only a few macroscopic degrees of freedom? (That sounds like a central limit theorem, some kind of result about how the large-scale limit is insensitive to all but a few aspects of the small scales.)

Historical issues: It's interesting to know how people have argued about this stuff.

See also: Statistical Mechanics; Nonequilibrium Statistical Mechanics; Maximum Entropy; Tsallis Statistics; Large Deviations; Concentration of Measure; Dynamical Systems (Including Chaos)