Related papers: Non-Ergodic Complexity Management
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
We consider non-ergodic class of stationary real harmonizable symmetric $\alpha$-stable processes $X=\left\{X(t):t\in\mathbb{R}\right\}$ with a finite symmetric and absolutely continuous control measure. We refer to its density function as…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
The calculation of observable averages in non-equilibrium regimes is one of the most important problems in statistical physics. Using the Hamiltonian approach of nonlinear response theory, we obtain a series expansion of the average excess…
Chemical affinities are responsible for driving active matter systems out of equilibrium. At the nano-scale, molecular machines interact with the surrounding environment and are subjected to external forces. The mechano-chemical coupling…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by…
The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…
We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum…
Understanding how systems respond to external perturbations is fundamental to statistical physics. For systems far from equilibrium, a general framework for response remains elusive. While progress has been made on the linear response of…
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…
In reinforcement learning, we typically aim to optimize the expected value of the sum of rewards an agent collects over a trajectory. However, if the process generating these rewards is non-ergodic, the expected value, i.e., the average…
In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian Mean Field model and show that the life-time of…