[show abstract][hide abstract] ABSTRACT: Consider a gas confined to the left half of a container. Then remove the
wall separating the two parts. The gas will start spreading and soon be
evenly distributed over the entire available space. The gas has
approached equilibrium. Why does the gas behave in this way? The
canonical answer to this question, originally proffered by Boltzmann, is
that the system has to be ergodic for the approach to equilibrium to
take place. This answer has been criticised on different grounds and is
now widely regarded as flawed. In this paper we argue that these
criticisms have dismissed Boltzmann's answer too quickly and that
something almost like Boltzmann's answer is true: the approach to
equilibrium takes place if the system is epsilon-ergodic, i.e. ergodic
on the entire accessible phase space except for a small region of
measure epsilon. We introduce epsilon-ergodicity and argue that relevant
systems in statistical mechanics are indeed espsilon-ergodic.
[show abstract][hide abstract] ABSTRACT: Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.