3: Ergodicity and the Approach to Equilibrium

3.1: Modeling the Approach to Equilibrium
3.2: Phase Flows in Classical Mechanics
3.3: Irreversibility and Poincaré Recurrence
The dynamics of the master equation describe an approach to equilibrium. These dynamics are irreversible: dH/dt≤0 , where H is Boltzmann’s H -function. However, the microscopic laws of physics are (almost) time-reversal invariant, so how can we understand the emergence of irreversibility?
3.4: Remarks on Ergodic Theory
3.5: Thermalization of Quantum Systems
3.6: Appendices
3.S: Summary

Thumbnail: Time evolution of two immiscible fluids. The local density remains constant.