A derivation of the master equation from path entropy maximization

Julian Lee, Steve Pressé

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13 Scopus citations

Abstract

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive nth-order Markov processes and the master equation as unique solutions to an inverse problem. We find that when constraints are not enough to uniquely determine the stochastic model, an nth-order Markov process emerges as the unique maximum entropy solution to this otherwise underdetermined problem. This gives a rigorous alternative for justifying such models while providing a systematic recipe for generalizing widely accepted stochastic models usually assumed to follow from the first principles.

Original languageEnglish (US)
Article number074103
JournalJournal of Chemical Physics
Volume137
Issue number7
DOIs
StatePublished - Aug 21 2012
Externally publishedYes

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ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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