Time, Statistical Mechanics, Thermodynamics

Lanford's theorem#

Boltzmann’s H-theorem and its modern versions (Lanford's theorem) show that for most microstates away from equilibrium, entropy increases in both time directions.

 A result by Lanford (1975, 1976, 1981) shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model.

It is widely believed that the work by Oscar E. Lanford (1975, 1976, 1981) provides the best available candidate for a rigorous derivation of the Boltzmann equation and the H-theorem from statistical mechanics, in the limiting case of an infinitely diluted gas system described by the hard spheres model, at least for a very brief time. To be sure, these clauses imply that Lanford’s result will hardly apply to realistic circumstances. The importance of Lanford’s theorem is that it claims to show how the conceptual gap between macroscopic irreversibility and microscopic reversibility can in principle be overcome, at least in simple cases.

Time's Arrow is Perspectival#

Is Time's Arrow Perspectival? (pdf)

I argue that for any generic microstate of a sufficiently rich system there are always special subsystems defining a coarse graining for which the entropy of the rest is low in one time direction (the "past"). These are the subsystems allowing creatures that "live in time" ---such as those in the biosphere--- to exist.