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Register a new userDynamical Phase Transitions for Flows on Finite Graphs
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Added by
D.R. Michiel Renger
Publication date
2020
fields
Physics
and research's language is
English
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We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.
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(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of information theory. Information theory provides a thermodynamically-consistent treatment of finite, open, transient and expanding systems which are difficult problems in approaches using standard statistical ensembles. As an example, we analyze is the problem of boundary conditions, which in the framework of information theory must also be treated statistically. We recall that out of the thermodynamical limit the different ensembles are not equivalent and in particular they may lead to dramatically different equation of states, in the region of a first order phase transition. We recall the recent progresses achieved in the understanding of first-order phase transition in finite systems: the equivalence between the Yang-Lee theorem and the occurrence of bimodalities in the intensive ensemble and the presence of inverted curvatures of the thermodynamic potential of the associated extensive ensemble.
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