On the arrow of time (Q478914)

The old physical paradox -- the irreversibility of thermodynamic processes, and increasing of entropy are investigated using numerical calculation of dynamic equations of gas molecules. The well-known Poincaré recurrence theorem is discussed using arguments that are based on non-integrable properties of gas molecules equations. The authors remark that transitions from one thermodynamic equilibrium to another can be realized by two types of chaotic dynamics of gas molecules. The Lyapunov exponents are computed for several sizes of perturbation and numbers of particles. The authors are reminding that there are two types of chaotic dynamics of gas molecules when the whole system moves from one thermodynamic equilibrium to another. From numerical experiments, they conclude that reversibility depends on the number of particles, their size and the computer accuracy.