The approach towards equilibrium in Lanford’s theorem

European Journal for Philosophy of Science 4 (3):309-335 (2014)
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This paper develops a philosophical investigation of the merits and faults of a theorem by Lanford , Lanford , Lanford for the problem of the approach towards equilibrium in statistical mechanics. Lanford’s result shows that, under precise initial conditions, the Boltzmann equation can be rigorously derived from the Hamiltonian equations of motion for a hard spheres gas in the Boltzmann-Grad limit, thereby proving the existence of a unique solution of the Boltzmann equation, at least for a very short amount of time. We argue that, by establishing a statistical H-theorem, it offers a prospect to complete Boltzmann’s combinatorial argument, without running against the objections which plug other typicality-based approaches. However, we submit that, while recovering the irreversible approach towards equilibrium for positive times, it fails to predict a monotonic increase of entropy for negative times, and hence it yields the wrong retrodictions about the past evolution of a gas



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Laws of Nature as Constraints.Emily Adlam - 2022 - Foundations of Physics 52 (1):1-41.
On How to Approach the Approach to Equilibrium.Joshua Luczak - 2016 - Philosophy of Science 83 (3):393-411.
Philosophy of statistical mechanics.Lawrence Sklar - 2008 - Stanford Encyclopedia of Philosophy.

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Time’s arrow and Archimedes’ point.Huw Price - 1996 - Philosophical and Phenomenological Research 59 (4):1093-1096.
The “Past Hypothesis”: Not even false.John Earman - 2006 - Studies in History and Philosophy of Modern Physics 37 (3):399-430.
Time's Arrow and Archimedes' Point: New Directions for the Physics of Time.Huw Price - 1998 - British Journal for the Philosophy of Science 49 (1):135-159.

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