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Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work,…
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…
We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the…
A review of the authors's results is given. Several methods are discussed for solving nonlinear equations $F(u)=f$, where $F$ is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy…
Equilibrium statistical mechanics provides a robust framework for characterizing phase transitions in systems whose microsopic dynamics are time-reversible. Efforts to develop and validate theoretical frameworks for time-irreversible,…
For a quantum system undergoing non-Markovian open quantum dynamics, we demonstrate a tomography algorithm based on multi-time measurements of the system, which reconstructs a minimal environment coupled to the system, such that the system…
Non-intrusive reduced-order modeling techniques are necessary for systems that are simulated using black-box solvers or known only from data. For systems exhibiting large transients and operating far away from equilibria, current…
The collective properties of small material systems considered as semidynamical systems revealing the Markov-type irreversible evolution, are investigated. It is shown that these material systems admit their treatment as thermodynamic…
Modeling count-valued time series has been receiving increasing attention since count time series naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from observing its inputs and outputs. Despite the huge effort made to study…
We study dynamical reversibility in stationary stochastic processes from an information theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional…
We consider in discrete time, a general class of sequential stochastic dynamic games with asymmetric information with the following features. The underlying system has Markovian dynamics controlled by the agents' joint actions. Each agent's…
We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact…
We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two…
A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing…