NDLI: Markov processes follow from the principle of maximum caliber

Content Provider	PubMed Central
Author	Ge, Hao Steve, Pressé Ghosh, Kingshuk Dill, Ken A.
Copyright Year	2012
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.
Related Links	http://dx.doi.org/10.1063/1.3681941
Starting Page	64108
File Format	PDF
ISSN	00219606
e-ISSN	10897690
Journal	The Journal of Chemical Physics
Issue Number	6
Volume Number	136
Language	English
Publisher	American Institute of Physics
Publisher Date	2012-01-01
Access Restriction	Open
Rights Holder	American Institute of Physics
Subject Keyword	Physical and Theoretical Chemistry Physics and Astronomy(all) Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Medicine Physical and Theoretical Chemistry

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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