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Quadratic and rate-independent limits for a large-deviations functional

Abstract

We construct a stochastic model showing the relationship between noise, gradient flows and rate-independent systems. The model consists of a one-dimensional birth–death process on a lattice, with rates derived from Kramers’ law as an approximation of a Brownian motion on a wiggly energy landscape. Taking various limits, we show how to obtain a whole family of generalized gradient flows, ranging from quadratic to rate-independent ones, connected via ‘L log L’ gradient flows. This is achieved via Mosco-convergence of the renormalized large-deviations rate functional of the stochastic process.

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Correspondence to Giovanni A. Bonaschi.

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Communicated by Andreas Öchsner.

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Bonaschi, G.A., Peletier, M.A. Quadratic and rate-independent limits for a large-deviations functional. Continuum Mech. Thermodyn. 28, 1191–1219 (2016). https://doi.org/10.1007/s00161-015-0470-1

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  • DOI: https://doi.org/10.1007/s00161-015-0470-1

Keywords

  • Large deviations
  • Gamma convergence
  • Gradient flows
  • Markov chains
  • Rate-independent systems