An important contemporary version of Boltzmannian statistical mechanics explains the approach to equilibrium in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognized as such and not clearly distinguished. This article identifies three different versions of typicality‐based explanations of thermodynamic‐like behavior and evaluates their respective successes. The conclusion is that the first two are unsuccessful because they fail to take the system's dynamics into account. The third, however, is promising. (...) I give a precise formulation of the proposal and present an argument in support of its central contention. †To contact the author, please write to: Department of Philosophy, Logic, and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, England; e‐mail: [email protected]. (shrink)

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. (shrink)

It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford 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. Here, we examine how and in what sense Lanford’s theorem (...) succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford’s theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all. (shrink)