Related papers: Stochastic action principle and maximum entropy
A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their…
A path information is defined in connection with the probability distribution of paths of nonequilibrium hamiltonian systems moving in phase space from an initial cell to different final cells. On the basis of the assumption that these…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
We develop an information-theoretic formulation of stochastic dynamics in which the fundamental stochastic variable is the total action connecting spacetime points, rather than individual paths. By maximizing Shannon entropy over a joint…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…
This work is an analytical calculation of the path probability for random dynamics of mechanical system described by Langevin equation with Gaussian noise. The result shows an exponential dependence of the probability on the action. In the…
This is an attempt to address diffusion phenomena from the point of view of information theory. We imagine a regular hamiltonian system under the random perturbation of thermal (molecular) noise and chaotic instability. The irregularity of…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…
We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular)…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
After the justification of the maximum entropy approach for equilibrium thermodynamic system, and of a maximum path entropy algorithm for nonequilibrium thermodynamic systems by virtue of the principle of virtual work, we present in this…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
The problem of the insensitivity of the macroscopic behavior of any thermodynamical system to partitioning generates a bias between the reproducibility of its macroscopic behavior viewed as the simplest form of causality and its long-term…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
In the real world, one almost never knows the parameters of a thermodynamic process to infinite precision. Reflecting this, here we investigate how to extend stochastic thermodynamics to systems with uncertain parameters, including…