Abstract
For the continuous time Markov processes we are concentrating on now, there is a unique stationary distribution \(\rho \) which is reached exponentially fast in time and uniformly so over all initial conditions.
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Notes
- 1.
But there is some algorithm, where the static fluctuation functional becomes the solution of a Hamilton-Jacobi equation, see [24, 25]. In equilibrium we have the macroscopic static fluctuation theory of Boltzmann-Planck-Einstein. It is still very instructive to read the first pages of [27] to get an early review. Later reviews for the macroscopic fluctuation theory in equilibrium are for example [28–30].
- 2.
Otherwise, we must introduce also surface tensions and the scaling could be with the surface of the subsystem and not with its volume.
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Maes, C. (2018). On the Stationary Distribution. In: Non-Dissipative Effects in Nonequilibrium Systems. SpringerBriefs in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-67780-4_3
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DOI: https://doi.org/10.1007/978-3-319-67780-4_3
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