Newtonian Dynamics from the Principle of Maximum Caliber

González, Diego López; Davis, Sergio; Gutiérrez, Gonzalo

doi:10.1007/s10701-014-9819-8

Cited by 21 publications

(25 citation statements)

References 13 publications

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“…This result for the particular case of a one-dimensional particle in a potential was obtained, in discretized form, in Ref. [12], and shows that the ensemble of trajectories follows Newton's law of motion,…”

Section: Dynamical Systems and The Functional Version Of Cvtsupporting

confidence: 54%

Applications of the divergence theorem in Bayesian inference and MaxEnt

Davis¹,

Gutiérrez²

2016

AIP Conference Proceedings

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Abstract. Given a probability density P(x|λ), where x represents continuous degrees of freedom and λ a set of parameters, it is possible to construct a general identity relating expectations of observable quantities, which is a generalization of the equipartition theorem in Thermodynamics.In this work we explore some of the consequences of this relation, both in the context of sampling distributions and Bayesian posteriors, and how it can be used to extract some information without the need for explicit calculation of the partition function (or the Bayesian evidence, in the case of posterior expectations). Together with the general family of fluctuation theorems it constitutes a powerful tool for Bayesian/MaxEnt problems.

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Section: Dynamical Systems and The Functional Version Of Cvtsupporting

confidence: 54%

Applications of the divergence theorem in Bayesian inference and MaxEnt

Davis¹,

Gutiérrez²

2016

AIP Conference Proceedings

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“…The first term in the above equation is referred to as the Boltzmann-Shannon-Gibbs (BSG) entropy, which has been applied in multiple fields, ranging from condensed matter physics [14] to finance [26,8]. Along with its path equivalent, maximum caliber [16], it has been successfully used to derive statistical mechanics [17], non-relativistic quantum mechanics, Newton's laws and Bayes' rule [16,9]. Under the axioms of consistency, uniqueness, invariance under coordinate transformations, sub-set and system independence, it can be proved that for constraints in the form of expected values, drawing self-consistent inferences requires maximising the entropy [33,29].…”

Section: Estimating the Log Determinant Using Maximum Entropymentioning

confidence: 99%

Entropic Trace Estimates for Log Determinants

Fitzsimons

Granziol

Cutajar

et al. 2017

Lecture Notes in Computer Science

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Abstract. The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework of maximum entropy, given information in the form of moment constraints from stochastic trace estimation. The estimates demonstrate a significant improvement on state-of-the-art alternative methods, as shown on a wide variety of UFL sparse matrices. By taking the example of a general Markov random field, we also demonstrate how this approach can significantly accelerate inference in large-scale learning methods involving the log determinant.

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“…The probability of these cases, calculated via Eqs. (7) and (8), are shown in table I. There we can see that the probability of the paths with higher action decrease extremely fast if η is large.…”

Section: The Principle Of Least Action As a Consequence Of Maxcalmentioning

confidence: 84%

“…We have to mention that, although we have compared Eqs. (7) and (10), their meanings are not the same. Eq.…”

Section: The Principle Of Least Action As a Consequence Of Maxcalmentioning

confidence: 99%

Principle of maximum caliber and quantum physics

General

2018

Phys. Rev. E

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MaxCal is a variational principle that can be used to infer distributions of paths in the phase space of dynamical systems. It has been successfully applied to different areas of classical physics, in particular statistical mechanics in and out of equilibrium. In this work, guided by the analogy of the formalism of MaxCal with that of the path integral formulation of quantum mechanics, we explore the extension of its applications to the realm of quantum physics, and show how the Lagrangians of both relativistic and nonrelativistic quantum fields can be built from MaxCal, with a suitable set of constraints. Related, the details of the constraints allow us to reinterpret the concept of inertia.

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Newtonian Dynamics from the Principle of Maximum Caliber

Cited by 21 publications

References 13 publications

Applications of the divergence theorem in Bayesian inference and MaxEnt

Applications of the divergence theorem in Bayesian inference and MaxEnt

Entropic Trace Estimates for Log Determinants

Principle of maximum caliber and quantum physics

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