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The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics…
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 deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
In this paper we consider the dynamics of harmonically-confined atomic gases. We present various general results which are independent of particle statistics, interatomic interactions and dimensionality. Of particular interest is the…
We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
A driven stochastic system in a constant temperature heat bath relaxes into a steady state which is characterized by the steady state probability distribution. We investigate the relationship between the driving force and the steady state…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…
We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within…
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…
In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy,…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
We propose a statistical mechanics for a general class of stationary and metastable equilibrium states. For this purpose, the Gibbs extremal conditions are slightly modified in order to be applied to a wide class of non-equilibrium states.…