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Maximum caliber inference of nonequilibrium processes

Source: J. Chem. Phys. 133, 034119 (2010); doi:10.1063/1.3455333

Published 21 July 2010

KEYWORDS and PACS
Keywords
PACS
  • 82.20.Wt
    Computational modeling and simulation of chemical kinetics
  • 82.20.Db
    Transition state theory and statistical theories of rate constants (chemical kinetics)
  • 02.30.Xx
    Calculus of variations
  • 02.60.-x
    Numerical approximation and analysis
  • 02.50.Ga
    Markov processes
  • YEAR: 2010
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PUBLICATION DATA
ISSN:
1553-9628 (online)
Publisher:
AIP is a member of CrossRef AIP
Moritz Otten and Gerhard Stock
Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays. ©2010 American Institute of Physics
History: Received 26 March 2010; accepted 28 May 2010; published 21 July 2010
Permalink: http://link.aip.org/link/?JCPSA6/133/034119/1

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