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A new approach to the approach to equilibrium

In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. The Frontiers Collection. Springer. pp. 99-114 (2012)

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  1. Essentially Ergodic Behaviour.Paula Reichert - forthcoming - British Journal for the Philosophy of Science:axaa007.
    I will prove a theorem on the precise connection of the time and phase-space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively ergodic. Explicitly, I will show that given a dynamical system with a stationary measure and a region of overwhelming phase-space measure, almost all trajectories spend almost all of their time in that region. Conversely, given that almost all trajectories spend almost all of (...)
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  • When Does a Boltzmannian Equilibrium Exist?Charlotte Werndl & Roman Frigg - 2016 - In Daniel Bedingham, Owen Maroney & Christopher Timpson (eds.), Quantum Foundations of Statistical Mechanics. Oxford, U.K.: Oxford University Press.
    The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we address these questions from the vantage point of the long-run fraction of time definition of Boltzmannian equilibrium that we developed in two recent papers. After a short summary of Boltzmannian statistical mechanics and our definition of equilibrium, we state an existence theorem which provides general (...)
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  • Reconceptualising Equilibrium in Boltzmannian Statistical Mechanics and Characterising its Existence.Charlotte Werndl & Roman Frigg - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49:19-31.
    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 (...)
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