Non-equilibrium Statistical Mechanics

action-angle variables analytic approach to equilibrium arbitrary articulation point asymptotic Balescu Boltzmann equation Brownian motion Chapter collision condition contribution coordinates correlations corresponding degrees of freedom density dependence derived destruction region diagonal fragments diagrams of Fig duration eigenfunctions energy equilibrium statistical mechanics evolution example expression factor finite Fokker-Planck equation formula Fourier coefficients Fourier transform H-theorem Hamiltonian hydrodynamic inhomogeneity integral interaction introduce invariants k₁ kk'k Laguerre polynomials Let us consider Liouville equation Liouville operator master equation matrix element molecular molecular chaos molecules momenta N-body problem normal modes notation obtain oscillators P₁ particles phase space Prigogine problem propagation quantum mechanics reduced distribution functions relation Résibois scattering singularity situations summation theorem theory tint transition unperturbed V₁ valid values vanishes variables velocity distribution function vertex wave vectors weakly coupled gases weakly coupled systems α α πδ ΣΣ