Markov processes follow from the principle of maximum caliber.

The Journal of Chemical Physics
Hao GeKen A Dill

Abstract

Markov models are widely used to describe stochastic dynamics. Here, we show that Markov models follow directly from the dynamical principle of maximum caliber (Max Cal). Max Cal is a method of deriving dynamical models based on maximizing the path entropy subject to dynamical constraints. We give three different cases. First, we show that if constraints (or data) are given in the form of singlet statistics (average occupation probabilities), then maximizing the caliber predicts a time-independent process that is modeled by identical, independently distributed random variables. Second, we show that if constraints are given in the form of sequential pairwise statistics, then maximizing the caliber dictates that the kinetic process will be Markovian with a uniform initial distribution. Third, if the initial distribution is known and is not uniform we show that the only process that maximizes the path entropy is still the Markov process. We give an example of how Max Cal can be used to discriminate between different dynamical models given data.

References

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Citations

Oct 5, 2013·The Journal of Chemical Physics·Taylor Firman, Kingshuk Ghosh
Aug 28, 2012·The Journal of Chemical Physics·Julian Lee, Steve Pressé
Sep 5, 2014·Biophysical Journal·Bochong Li, Lingchong You
Aug 10, 2015·The Journal of Chemical Physics·Michael J HazoglouKen A Dill
Oct 3, 2017·PLoS Computational Biology·Vahid RostamiMoritz Helias
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Julian Lee, Steve Pressé
Dec 15, 2016·Physical Review. E·Carlo Cafaro, Sean Alan Ali
Jan 8, 2018·The Journal of Chemical Physics·Purushottam D DixitKen A Dill
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Purushottam D Dixit
May 20, 2018·Physical Review. E·Julian Lee
Feb 23, 2020·Annual Review of Physical Chemistry·Kingshuk GhoshKen A Dill
Aug 17, 2020·Physical Review. E·Riccardo Marcaccioli, Giacomo Livan
Nov 9, 2017·Biophysical Journal·Taylor FirmanKingshuk Ghosh
Jun 6, 2014·The Journal of Physical Chemistry. B·Steve PresséKen Dill

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Software Mentioned

Max Cal
Max

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