Probability in Classical Statistical Mechanics

Probability in Boltzmannian Statistical Mechanics

Ergodic hypothesis in classical statistical mechanics

An updated discussion on physical and mathematical aspects of the ergodic hypothesis in classical equilibrium statistical mechanics is presented. Then a practical attitude for the justification of the microcanonical ensemble is indicated. It is also remarked that the difficulty in proving the ergodic hypothesis should be expected.

Nonequilibrium Statistical Mechanics of Open Classical Systems

We describe the ergodic and thermodynamical properties of chains of anharmonic oscillators coupled, at the boundaries, to heat reservoirs at positive and different temperatures. We discuss existence and uniqueness of stationary states, rate of convergence to stationarity, heat flows and entropy production, Kubo formula and Gallavotti-Cohen fluctuation theorem.

Classical Statistical Mechanics and Landau Damping

We study the retarded response function in scalar φ4-theory at finite temperature. We find that in the high-temperature limit the imaginary part of the self-energy is given by the classical theory to leading order in the coupling. In particular the plasmon damping rate is a purely classical effect to leading order, as shown by Aarts and Smit. The dominant contribution to Landau damping is given...

Statistical mechanics of quantum-classical systems

The statistical mechanics of systems whose evolution is governed by mixed quantum-classical dynamics is investigated. The algebraic properties of the quantum-classical time evolution of operators and of the density matrix are examined and compared to those of full quantum mechanics. The equilibrium density matrix that appears in this formulation is stationary under the dynamics and a method for...