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The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge…
In this work we develop on the recently suggested concept of superstatistics [C. Beck and E.G.D. Cohen, Physica A {\bf 322}, 267 (2003)], face the problem of devising a viable way for estimating the correct statistics for a system in…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Using techniques from stochastic thermodynamics, we derive…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
The most rigorous physical description of non-equilibrium gas dynamics is rooted in the numerical solution of the Boltzmann equation. Yet, the large number of degrees of freedom and the wide range of both spatial and temporal scales render…
Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…
Turbulence may appear as a complex process with a multitude of scales and flow patterns, but still obeys simple physical principles such as the conservation of momentum, of energy, and the maximum entropy principle. The latter states that…
A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to…
A principle of hierarchical entropy maximization is proposed for generalized superstatistical systems, which are characterized by the existence of three levels of dynamics. If a generalized superstatistical system comprises a set of…
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,…
We propose a geometric theory of non-equilibrium thermodynamics, namely geometric thermodynamics, using our recent developments of differential-geometric aspects of entropy production rate in non-equilibrium thermodynamics. By revisiting…
We develop a new theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of non-equilibrium statistical mechanics. The general form of the many-body density matrix is…
A stochastic action principle for stochastic dynamics is revisited. We present first numerical diffusion experiments showing that the diffusion path probability depend exponentially on average Lagrangian action. This result is then used to…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…