A New Approach to the Approach to Equilibrium

Frigg, Roman; Werndl, Charlotte

doi:10.1007/978-3-642-21329-8_7

Cited by 7 publications

(1 citation statement)

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“…The notion that equilibrium is defined by the largest macro-region (where 'largest' can mean either β-dominant or δ-prevalent) is deeply entrenched in BSM, and it is shared by rivalling versions of BSM. Those who favour an account of BSM based on ergodic theory have to assume that Z Meq is large because otherwise the system would not spend most of its time in equilibrium (see, for instance, Frigg and Werndl 2011a, 2012a, 2012b. Those who see the approach to equilibrium as result of some sort of probabilistic dynamics assume that Z Meq is large because they assign probabilities to macro-states that are proportional to µ E (Γ M ) and equilibrium comes out as the most likely state only if the equilibrium macro-region is large (e.g.…”

Section: Defining Equilibrium: Conceptual Quandariesmentioning

confidence: 99%

Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence

Werndl

Frigg

2015

Studies in History and Philosophy of Science Part B: Studies in

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In Boltzmannian statistical mechanics macro-states supervene on microstates. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. 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 macro-region is the largest macro-region. 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 macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem.

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Section: Defining Equilibrium: Conceptual Quandariesmentioning

confidence: 99%