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 language | English (US) |
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Article number | 074103 |
Journal | Journal of Chemical Physics |
Volume | 137 |
Issue number | 7 |
DOIs | |
State | Published - Aug 21 2012 |
Externally published | Yes |
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry