Repository: Freie Universität Berlin, Math Department

Variational structures beyond gradient flows: a macroscopic fluctuation-theory perspective

Patterson, Robert I.A. and Renger, D.R. Michiel and Sharma, Upanshu (2021) Variational structures beyond gradient flows: a macroscopic fluctuation-theory perspective. arXive . pp. 1-47. (Unpublished)

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Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the density of the particle system. While large deviations can be studied in considerable generality, these variational structures are often restricted to systems in detailed balance. Using insights from macroscopic fluctuation theory, in this work we aim to generalise this variational connection beyond dissipative systems by augmenting densities with fluxes, which encode non-dissipative effects. Our main contribution is an abstract framework, which for a given flux-density cost and a quasipotential, provides a decomposition into dissipative and non-dissipative components and a generalised orthogonality relation between them. We then apply this abstract theory to various stochastic particle systems – independent copies of jump processes, zero-range processes, chemical-reaction networks in complex balance and lattice-gas models.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2564
Deposited By: Monika Drueck
Deposited On:29 Apr 2021 09:49
Last Modified:29 Apr 2021 09:49

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