Weakly Non-Ergodic Statistical Physics

Physics 127c: Statistical Mechanics Weakly Interacting Fermi Gas

and defines the spectrum. The value of vF is altered by interactions. The familiar spectrum leads to the usual temperature dependences at low temperature, e.g. specific heat C ∝ T , susceptibility χ independent of temperature. Furthermore, since there is no qualitative change of behavior, unlike for the Boson case (where the canonical transformation was necessary) quantitative results can be ca...

Ergodic theorem, ergodic theory, and statistical mechanics.

This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...

Fluctuation relation for weakly ergodic aging systems.

A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connect...

Four Lectures on Non-Equilibrium Statistical Physics

Statistical Physics