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Ergodicity, dissipation, and large-deviation theory in non-equilibrium systems

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The theory of stochastic thermodynamics connects the macroscopic world of thermodynamics with the dynamical fluctuations that necessarily occur on microscopic scales. We examine the behaviour associated with large rare fluctuations in which systems violate ergodicity. We show that in systems with particular symmetries, this can lead to peculiar steady states in which currents flow without dissipation [1,2]. We also consider other examples of rare events that violate ergodicity, focussing on simple interacting-particle systems [3].

[1] R. L. Jack and R. M. L. Evans, J. Stat. Mech. (2016) 093305. [2] R. L. Jack, M. Kaiser, and J. Zimmer, Entropy 19, 562 (2017). [3] R. L. Jack, I. R. Thompson and P. Sollich, Phys. Rev. Lett. 114, 060601 (2015).

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