Computation of entropy increase for Lorentz gas and hard disks

Maurice Courbage (1) , Seyed Majid Saberi Fathi (1)

1 MSC - Matière et Systèmes Complexes

Entropy functionals are computed for non-stationary distributions of particles of Lorentz gas and hard disks. The distributions consisting of beams of particles are found to have the largest amount of entropy and entropy increase. The computations show exponentially monotonic increase during initial time of rapid approach to equilibrium. The rate of entropy increase is bounded by sums of positive Lyapounov exponents.

Mots clés: H-Theorem; Entropy; Lyapounov Exponents; Collision Map; Hard Disks; Lorentz Gas

Domaines: Mécanique statistique [cond-mat.stat-mech]; Systèmes dynamiques [math.DS]; Dynamique Chaotique [nlin.CD]

Maurice Courbage, Seyed Majid Saberi Fathi. Computation of entropy increase for Lorentz gas and hard disks. Communications in Nonlinear Science and Numerical Simulation, 2008, 13 (2), pp.444-455. ⟨10.1016/j.cnsns.2006.05.007⟩. ⟨hal-00071675⟩