Abstract
Given the dynamics the initial state of the system has to be specified. From the point of view of statistical mechanics states are probability measures on the phase space Γ. The initial measure μ is transported along by the flow T t to the measure at time t as μ t = μ°T −t . If μ has a density f, μ(dNd q dNd p)= f(q, p)dNd q dNd p, then μ t (dNd q dNd p) = (f° T −t )(q, p) d Nd q dNd p. For stochastic boundary conditions the probability measure at time t is μ t (dNd q dNd p) = ∫μ(dd q’ dNd p’) P t (q’, p’|dNd q dNd p), t ≧ 0, according to the rules for Markov processes.
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© 1991 Springer-Verlag Berlin Heidelberg
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Spohn, H. (1991). States of Equilibrium and Local Equilibrium. In: Large Scale Dynamics of Interacting Particles. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84371-6_3
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DOI: https://doi.org/10.1007/978-3-642-84371-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-84373-0
Online ISBN: 978-3-642-84371-6
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