Related papers: Statistical Mechanics of Unconfined Systems: Chall…
We present a maximum entropy approach to analyze the internal dynamics of a small system in contact with a large bath e.g. a solute-solvent system. For the small solute, the fluctuations around the mean values of observables are not…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
We present a novel derivation of the constraints required to obtain the underlying principles of statistical mechanics using a maximum entropy framework. We derive the mean value constraints by use of the central limit theorem and the…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
This work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve…
We consider the transport of gas in long pipes and pipeline networks for which the dynamics are dominated by friction at the pipe walls. The governing equations can be formulated as an abstract dissipative Hamiltonian system which allows us…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
The kinetics of collisionless continuous medium is studied in a bounded region on a curved manifold. We have assumed that in statistical equilibrium, the probability distribution density depends only on the total energy. It is shown that in…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…