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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
Keywords Approach to equilibrium   Statistical mechanics   Boltzmann
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DOI 10.1007/s13194-014-0086-5
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The “Past Hypothesis”: Not Even False.John Earman - 2006 - Studies in History and Philosophy of Modern Physics 37 (3):399-430.
The Oxford Handbook of Philosophy of Physics.Robert W. Batterman (ed.) - 2013 - Oxford University Press USA.

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