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This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Understanding the universal properties of non-equilibrium phase transitions of spreading processes is a challenging problem. This applies in particular to irregular and dynamically varying networks. We here investigate an experimentally…
To study the impacts of price responsive demand on the electric power system requires better load models. This paper discusses the modeling of uncertainties in aggregated thermostatically controlled loads using a state queueing (SQ) model.…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
In this paper, we derive a generalized second fluctuation-dissipation theorem (FDT) for stochastic dynamical systems in the steady state. The established theory is built upon the Mori-type generalized Langevin equation for stochastic…
We study adaptive control of classical ergodic Hamiltonian systems, where the controlling parameter varies slowly in time and is influenced by system's state (feedback). An effective adiabatic description is obtained for slow variables of…
This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function…
We present a construction of non-equilibrium steady states in one-dimensional quantum critical systems carrying energy and charge fluxes. This construction is based on a scattering approach within a real-time hamiltonian reservoir…
We investigate the effective temperature of a harmonic chain whose two ends are coupled to two baths at different temperatures. We propose to take the weighted average temperature as the effective temperature of the system. The weight…
The increased model capacity of Diffusion Transformers (DiTs) and the demand for generating higher resolutions of images and videos have led to a significant rise in inference latency, impacting real-time performance adversely. While prior…
This paper is a survey of extensions to finite automata theory to model real-time systems as well as systems exhibiting mixed discrete-continuous behavior. Real-time systems maintain a continuous and timely interaction with the environment,…
Abstract: Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here a formal interpretation will be discussed of the widespread idea…
A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the $L^1$ distance of a function of the probability generating function of the model under the null…
We study stability of abstract differential equations coupled by means of a general algebraic condition. Our approach is based on techniques from operator theory and systems theory, and it allows us to study coupled systems by exploiting…
Multistable non-equilibrium systems are abundant outcomes of nonlinear dynamics with feedback but still relatively little is known about what determines the stability of the steady states and their switching rates in terms of entropy and…
We propose a variational framework for nonequilibrium thermodynamics built around the effective number of accessible state, a multiplicative count that ranges from for a uniform distribution to one under complete localization, and whose…
We study stability issue of reset and impulsive switched systems. We find time constraints (dwell time and flee time) on switching signals which stabilize a given reset switched system. For a given collection of matrices, we find an…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
Melting behaviors of defective crystals under extreme conditions are theoretically investigated using the statistical moment method. In our theoretical model, heating processes cause missing atoms or vacancies in crystal structures via…
We discuss a class of mechanical models of thermometers and their minimal requirements to determine the temperature for systems out of the common scope of thermometry. In particular we consider: 1) anharmonic chains with long time of…