Time-asymmetry paradox

Abstract

For a system in a nonequilibrium macrostate we may distinguish four classes of microstates: Microstates which evolve toward the equilibrium state in the forward-time direction but away from the equilibrium state in the backward-time direction, microstates which evolve away from the equilibrium state in the forward-time direction but toward the equilibrium state in the backward-time direction, microstates which evolve away from the equilibrium state in both time directions, and microstates which evolve toward the equilibrium state in both time directions. A simple system is examined, and the fraction of each of the four classes is determined. It is shown that in the thermodynamic limit all the states belong to the last of the four classes. It is also shown that a system evolving toward the equilibrium state will, with overwhelming probability, continue to evolve toward the equilibrium state.