Classical stochastic systems with fast-switching environments: Reduced master equations, their interpretation, and limits of validity

Peter G. Hufton, Yen Ting Lin, and Tobias Galla
Phys. Rev. E 99, 032121 – Published 15 March 2019

Abstract

We study classical Markovian stochastic systems with discrete states, coupled to randomly switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of infinite timescale separation. We show that this can lead to master equations with bursting events. Negative transition rates can result in the reduced master equation, leading to unphysical short-time behavior. However, the reduced master equation can describe stationary states better than a leading-order adiabatic calculation, similar to what is known for Kramers-Moyal expansions in the context of the Pawula theorem [R. F. Pawula, Phys. Rev. 162, 186 (1967); H. Risken and H. Vollmer, Z. Phys. B 35, 313 (1979)]. We provide an interpretation of the reduced dynamics in discrete time and a criterion for the occurrence of negative rates for systems with two environmental states.

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  • Received 8 March 2018
  • Revised 14 January 2019

DOI:https://doi.org/10.1103/PhysRevE.99.032121

©2019 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsStatistical Physics & ThermodynamicsInterdisciplinary Physics

Authors & Affiliations

Peter G. Hufton1, Yen Ting Lin1,2, and Tobias Galla1

  • 1Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
  • 2Center for Nonlinear Studies and Theoretical and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Issue

Vol. 99, Iss. 3 — March 2019

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