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<Hugo Touchette> develops connections between the <large deviation principle> and <statistical mechanics>. Rare fluctuations often have probabilities that decrease exponentially with system size or observation time; their <rate function> captures information beyond a local Gaussian approximation. His treatment uses this structure to derive variational descriptions of equilibrium and nonequilibrium states. Nonconcave entropies expose limits of ordinary <Legendre transforms> and help explain why different statistical ensembles need not be equivalent.<The large deviation approach to statistical mechanics by Hugo Touchette>[Physics Reports 478, 1–69 (2009), abstract and equilibrium/nonequilibrium variational formulations]{ref}

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Hugo Touchette

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