A derivation of the master equation from path entropy maximization

Julian Lee, Steve Pressé

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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
Issue number7
StatePublished - Aug 21 2012
Externally publishedYes

ASJC Scopus subject areas

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


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