Related papers: Maximum Caliber and quantum physics
We review here {\it Maximum Caliber} (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of {\it Maximum Entropy} (Max…
There has been interest in finding a general variational principle for non-equilibrium statistical mechanics. We give evidence that Maximum Caliber (Max Cal) is such a principle. Max Cal, a variant of Maximum Entropy, predicts dynamical…
Maximum Caliber (Max Cal) is purported to be a general variational principle for Non-Equilibrium Statistical Physics (NESP). But recently, Jack and Evans and Maes have raised concerns about how Max Cal handles dissipative processes. Here,…
We investigate 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. Specifically, we…
Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to…
Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…
A modern notion of integrability is that of multidimensional consistency (MDC), which classically implies the coexistence of (commuting) dynamical flows in several independent variables for one and the same dependent variable. This property…
We study quantum caustics in $d$-dimensional systems with quadratic Lagrangians. Based on Schulman's procedure in the path-integral we derive the transition amplitude on caustics in a closed form for generic multiplicity $f$, and thereby…
A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical…
A permanent challenge in physics and other disciplines is to solve partial differential equations, thereby a beneficial investigation is to continue searching for new procedures to do it. In this Letter, a novel Monte-Carlo Metropolis…
We derive a closed-form geometric functional for kernel dynamics on finite graphs by applying the Maximum Caliber (MaxCal) variational principle to the spectral transfer function h(lambda) of the graph Laplacian eigenbasis. The main result…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
A direct reformulation of the Hamiltonian formalism in terms of the intrinsic geometry of infinitely prolonged differential equations is obtained. Concepts of spatial equation and spatial-gauge symmetry of a Lagrangian system of equations…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
We propose a variational framework in which the kernel function k : X x X -> R, interpreted as the foundational object encoding what distinctions an agent can represent, is treated as a dynamical variable subject to path entropy…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
We provide a new paradigm for quantum simulation that is based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…