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Good just isn’t good enough – Humean chances and Boltzmannian statistical physics
 In
, 2013
"... Abstract Statistical physicists assume a probability distribution over microstates to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. ..."
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Abstract Statistical physicists assume a probability distribution over microstates to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances.
The Best Humean System for Statistical Mechanics
, 2013
"... 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. ..."
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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. 1
This article is forthcoming in: Studies in History and Philosophy of Modern Physics
"... philosophyofsciencepartbstudiesinhistoryandphilosophyofmodernphysics/ A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measuretheoretic dynamical systems theory measures can similarly be interpreted as typicality ..."
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philosophyofsciencepartbstudiesinhistoryandphilosophyofmodernphysics/ A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measuretheoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky’s (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translationcontinuous or translationclose). The conclusion are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilonergodic, there are uniqueness results about typicality measures. 1 ar
Equilibrium Approach to equilibrium Boltzmann Statistical mechanics
, 2014
"... a b s t r a c t In Boltzmannian statistical mechanics macrostates supervene on microstates. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable microstates. The largest of these regions is singled out as the equilibrium region of the syste ..."
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a b s t r a c t In Boltzmannian statistical mechanics macrostates supervene on microstates. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable microstates. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in full generality – i.e. without making any assumptions about the system's dynamics or the nature of the interactions between its components – that the equilibrium macroregion is the largest macroregion. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another – again fully general – theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor (such as ergodicity or typicality), the focus should be on finding triplets of macrovariables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem.
Rethinking Boltzmannian Equilibrium
"... Boltzmannian statistical mechanics partitions the phase space of a system into macroregions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the MaxwellBoltzmann distribution, and maximum ent ..."
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Boltzmannian statistical mechanics partitions the phase space of a system into macroregions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the MaxwellBoltzmann distribution, and maximum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilibrium thus defined corresponds to the largest macroregion. Our derivation is completely general in that it does not rely on assumptions about a system’s dynamics or internal interactions. 1