Loschmidt's Paradox - Dynamical Systems

Dynamical Systems

Current research in dynamical systems offers one possible mechanism for obtaining irreversibility from reversible systems. The central argument is based on the claim that the correct way to study the dynamics of macroscopic systems is to study the transfer operator corresponding to the microscopic equations of motion. It is then argued that the transfer operator is not unitary (i.e. is not reversible) but has eigenvalues whose magnitude is strictly less than one; these eigenvalues corresponding to decaying physical states. This approach is fraught with various difficulties; it works well for only a handful of exactly solvable models.

Abstract mathematical tools used in the study of dissipative systems include definitions of mixing, wandering sets, and ergodic theory in general.