Poincaré, Poincaré recurrence and the H-theorem: A continued reassessment of Boltzmannian statistical mechanics

Abstract

In [C. G. Weaver Found. Phys. 51, 1 (2021)], I showed that Boltzmann’s [Formula: see text]-theorem does not face a significant threat from the reversibility paradox. I argue that my defense of the [Formula: see text]-theorem against that paradox can be used yet again for the purposes of resolving the recurrence paradox without having to endorse heavy-duty statistical assumptions outside of the hypothesis of molecular chaos. As in [C. G. Weaver Found. Phys. 51, 1 (2021)], lessons from the history and foundations of physics reveal precisely how such resolution is achieved.

Thermostatistics, Information, Subjectivity: Why Is This Association So Disturbing?

“…The other viewpoint is that this paradox basically raises the question of how, from time-symmetrical equations of motion (those of mechanics), it is possible to obtain timeasymmetrical results. The consensual answer [52,54,55] is that, within the ingredients that permit us to write the Boltzmann transport equation, the time asymmetry is already present in the form of the "hypothesis of molecular chaos": the velocities of two particles before their collision are fully uncorrelated but, of course, are fully correlated and determined by mechanics after the collision. Fundamentally, the Boltzmann transport equation (and thus the H-theorem) is obtained by moving the time asymmetry of the second law of thermodynamics from the macroscopic to the microscopic scale.…”

Thermostatistics, Information, Subjectivity, Why Is This Association So Disturbing?

“…The other viewpoint is that this paradox basically raises the question of how from time-symmetrical equations of motion (those of mechanics) it is possible to obtain time-asymmetrical results. The consensual answer [49,51,52] is that, within the ingredients that permit to write the Boltzmann transport equation, the time-asymmetry is already presents under the form of the "hypothesis of molecular chaos": the velocities of two particles before their collision are fully uncorrelated but of course fully correlated and determined by mechanics after the collision. Fundamentally, the Boltzmann transport equation (and thus the H-theorem) is obtained by moving the time asymmetry of the 2nd law of thermodynamics from the macroscopic to the microscopic scale.…”