The Justification of Probability Measures in Statistical Mechanics*

Abstract

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low-entropy macrostates are less probable than high-entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law is unhelpful at best and wrong at worst, and will argue that certain puzzles sometimes associated with the second law are merely artifacts of this questionable justification.

Foundations of Statistical Mechanics

“…Since nothing in what follows depends on the exact form of these distributions, we will not state them here. For formal definitions of these distributions, see, for instance, Tolman (1938Tolman ( /1979 and Lavis (2015), and for philosophical discussions, see Davey (2008Davey ( , 2009 and Myrvold (2016).…”

Equilibrium in Boltzmannian Statistical Mechanics

“…As Winsberg (2004) point out, just because the overall entropy of the universe increases, it need not be the case that the entropy in a small subsystem also increases and hence Albert's approach cannot explain the behaviour of small systems like gases in laboratories. Albert's argument relies on assigning probabilities to sets of microstates based on a certain algorithm, and there are questions about the justification of that algorithm (see Davey 2008 andFrigg 2010a). Furthermore, Albert's justification that a high entropy future and low entropy past are overwhelmingly likely appeals to a dynamical assumption, which he calls the 'scattering condition', and there is a question whether this condition holds true in SM systems.…”

Justifying typicality measures of Boltzmannian statistical mechanics and dynamical systems

“…The initial probability distributions of interest are a class P of translation-close probability distributions where for every open set A there is a p ∈ P with p(A) > 0. Davey (2008), Hemmo and Shenker (2012) and Leeds (1989) have criticised the extant foundational literature on Boltzmannian SM for assuming that the initial probability distribution is µ E and has to be invariant under the dynamics. They rightly argue that the initial probability distribution can be different from µ E and may well not be invariant under the dynamics.…”