Loschmidt's paradox

Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics. This puts the time reversal symmetry of (almost) all known low-level fundamental physical processes at odds with any attempt to infer from them the second law of thermodynamics which describes the behaviour of macroscopic systems. Both of these are well-accepted principles in physics, with sound observational and theoretical support, yet they seem to be in conflict; hence the paradox.

Johann Loschmidt's criticism was provoked by the H-theorem of Boltzmann, which was an attempt to explain using kinetic theory the increase of entropy in an ideal gas from a non-equilibrium state, when the molecules of the gas are allowed to collide. Loschmidt pointed out in 1876 that if there is a motion of a system from time t0 to time t1 to time t2 that leads to a steady decrease of H (increase of entropy) with time, then there is another allowed state of motion of the system at t1, found by reversing all the velocities, in which H must increase. This revealed that one of the key assumptions in Boltzmann's theorem was flawed, namely that of molecular chaos, that all the particle velocities were completely uncorrelated. One can assert that the correlations are uninteresting, and therefore decide to ignore them; but if one does so, one has changed the conceptual system, injecting an element of time-asymmetry by that very action.

Reversible laws of motion cannot explain why we experience our world to be in such a comparatively low state of entropy at the moment (compared to the equilibrium entropy of universal heat death); and to have been at even lower entropy in the past.