Werndl, Charlotte and Frigg, Roman (2015) Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence. [Preprint]
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Abstract
In Boltzmannian statistical mechanics macro-states supervene on micro-states. 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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| Item Type: | Preprint | |||||||||
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| Keywords: | equilibrium, existence of equilibrium, approach to equilibrium, thermodynamic-like behaviour, Boltzmann, ergodic, epsilon-ergodic, macrostates | |||||||||
| Subjects: | Specific Sciences > Physics > Classical Physics Specific Sciences > Physics Specific Sciences > Probability/Statistics Specific Sciences > Physics > Statistical Mechanics/Thermodynamics |
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| Depositing User: | Charlotte Werndl | |||||||||
| Date Deposited: | 18 Sep 2015 21:09 | |||||||||
| Last Modified: | 18 Sep 2015 21:09 | |||||||||
| Item ID: | 11685 | |||||||||
| Subjects: | Specific Sciences > Physics > Classical Physics Specific Sciences > Physics Specific Sciences > Probability/Statistics Specific Sciences > Physics > Statistical Mechanics/Thermodynamics |
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| Date: | 2015 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/11685 |
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