Thermodynamic arrow of time

The temporal orientation associated with the typical increase of macroscopic entropy away from suitable low-entropy conditions. It is a statistical claim about specified initial or boundary conditions and a macroscopic description, rather than a universal monotonicity theorem for every microscopic trajectory. Time reversal in classical mechanics pairs suitable increasing trajectories with decreasing ones, while fine-grained entropy is conserved under regular volume-preserving Hamiltonian flow.

The hypothesis of a special low-entropy boundary condition in the past, used in statistical accounts of the thermodynamic arrow of time. A complete account must also state its probability measure over compatible microstates and the macroscopic description used to define entropy.