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Cocke, W.J., 1967: Statistical time symmetry and two-time boundary conditions in physics and cosmology. Phys. Rev., 160, 1165-1170, doi:10.1103/PhysRev.160.1165.
The hypothesis of complete time symmetry in oscillating cosmologies in which there exist locally irreversible processes is examined. A time-symmetric formalism for purely statistical processes is developed, and all aspects of quantum and statistical mechanics are shown to be time-symmetric within this framework. We conclude from analysis of a simple example that in a completely time-symmetric oscillating cosmology, statistical processes which produce entropy in the expanding phase will reverse themselves in the contracting phase, although microscopic reversal of motion need not occur. The analysis provides a self-consistent formalism for general problems involving the coexistence of different entropic directions of time in the observable universe. Boltzmann's H theorem is discussed in this framework.
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