Hamiltonian formalism and path entropy maximization

  title={Hamiltonian formalism and path entropy maximization},
  author={Sergio M. Davis and Diego L. Gonz'alez},
  journal={Journal of Physics A: Mathematical and Theoretical},
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous constraints on position and velocity, a Lagrangian emerges which determines the most probable trajectory. Deviations from the probability maximum can be consistently described as slices in time by a Hamiltonian, according to a nonlinear Langevin equation and its… 

Predictive Statistical Mechanics and Macroscopic Time Evolution: Hydrodynamics and Entropy Production

In the previous papers (Kuić et al. in Found Phys 42:319–339, 2012; Kuić in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the

Predictive Statistical Mechanics and Macroscopic Time Evolution: Hydrodynamics and Entropy Production

In the previous papers (Kuić et al. in Found Phys 42:319–339, 2012; Kuić in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the

Continuity equation for probability as a requirement of inference over paths

Local conservation of probability, expressed as the continuity equation, is a central feature of non-equilibrium Statistical Mechanics. In the existing literature, the continuity equation is always

Jarzynski equality in the context of maximum path entropy

In the global framework of finding an axiomatic derivation of nonequilibrium Statistical Mechanics from fundamental principles, such as the maximum path entropy -- also known as Maximum Caliber

Maximum caliber inference and the stochastic Ising model.

This work investigates the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information and finds that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier leads to a formal overlap with well-known Glauber hyperbolic tangent rule.

Principle of maximum caliber and quantum physics.

This work shows how the Lagrangians of both relativistic and nonrelativistic quantum fields can be built from MaxCal, with a suitable set of constraints, and reinterpreted the concept of inertia.

Solving Equations of Motion by Using Monte Carlo Metropolis: Novel Method Via Random Paths Sampling and the Maximum Caliber Principle

A novel Monte Carlo Metropolis framework is presented for solving the equations of motion in Lagrangian systems and can be general enough to solve other differential equations in physics and a useful tool to calculate the time-dependent properties of dynamical systems in order to understand the non-equilibrium behavior of statistical mechanical systems.

Expectation values of general observables in the Vlasov formalism

Collisionless plasmas in an arbitrary dynamical state are described by the Vlasov equation, which gives the time evolution of the probability density ρ(x, v). In this work we introduce a new

Entropic Dynamics on Gibbs Statistical Manifolds

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Liouville’s theorem from the principle of maximum caliber in phase space

One of the cornerstones in non–equilibrium statistical mechanics (NESM) is Liouville’s theorem, a differential equation for the phase space probability ρ(q, p; t). This is usually derived considering

Conjugate variables in continuous maximum-entropy inference.

  • S. DavisG. Gutiérrez
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
A general relation connecting the Lagrange multipliers and the expectation values of certain particularly constructed functions of the states of the system is derived, which provides some insight into the interpretation of the hypervirial relations known in statistical mechanics and the recently derived microcanonical dynamical temperature.

Newtonian Dynamics from the Principle of Maximum Caliber

The foundations of Statistical Mechanics can be recovered almost in their entirety from the principle of maximum entropy. In this work we show that its non-equilibrium generalization, the principle

Hidden BRS invariance in classical mechanics. II.

An interpretation for the ghost fields as being the well-known Jacobi fields of classical mechanics is provided, and the Hamiltonian {ital {tilde H}}, derived from the action {ital{tilde S}}, turns out to be the Lie derivative associated with theHamiltonian flow.

Principles of maximum entropy and maximum caliber in statistical physics

The variational principles called maximum entropy (MaxEnt) and maximum caliber (MaxCal) are reviewed. MaxEnt originated in the statistical physics of Boltzmann and Gibbs, as a theoretical tool for

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Under the assumption that the underlying process is continuous Markovian and using simple short time correlation functions as constraints in the maximum calibre principle of Jaynes we derive the

The Minimum Entropy Production Principle

It seems intuitively reasonable that Gibbs' variational principle de­ termining the conditions of heterogeneous equilibrium can be gener­ alized to nonequilibrium conditions. That is, a

Derivation of the Schrodinger equation from Newtonian mechanics

We examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external

Entropy and the time evolution of macroscopic systems

1. Introduction 2. Some Clarification from Another Direction 3. The Probability Connection 4. Equilibrium Statistical Mechanics and Thermodynamics 5. The Presumed Extensivity of Entropy 6.

The Fokker-Planck Equation

In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for one

Fokker-Planck Equation

As shown in Sects. 3.1, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (3.1, 31). For nonlinear Langevin equations (3.67, 110) expectation