Related papers: Non-Ergodic Complexity Management
The issue of relaxation has been addressed in terms of ergodic theory in the past. However, the application of that theory to models of physical interest is problematic, especially when dealing with relaxation to nonequilibrium steady…
How biological networks achieve robust control despite relying on imperfect, local information remains an important open question. Here, we identify thermodynamic constraints that can curtail non-equilibrium steady-state responses so…
We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by the network directed links.…
Linear theory of stationary response in thermal systems subjected to external perturbations requires to find equilibrium correlation function of the responding system variable in the absence of external perturbations. Studies of the…
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances…
Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the response of nonequilibrium steady state…
In complex systems, crucial parameters are often subject to unpredictable changes in time. Climate, biological evolution and networks provide numerous examples for such non-stationarities. In many cases, improved statistical models are…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
The interpretation of experimental and numerical data describing off-equilibrium aging dynamics crucially depends on the connection between spontaneous and induced fluctuations. The hypothesis that linear response fluctuations are…
It is well known that quantum feedback can alter the dynamics of open quantum systems dramatically. In this paper, we show that non-ergodicity may be induced through quantum feedback and resultantly create system dynamics that have lasting…
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…
Dynamical ensembles have been introduced to study constrained stochastic processes. In the microcanonical ensemble, the value of a dynamical observable is constrained to a given value. In the canonical ensemble a bias is introduced in the…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
Many natural and technological systems fail to adapt to changing external conditions and move to a different state if the conditions vary too fast. Such "non-adiabatic" processes are ubiquitous, but little understood. We identify these…
Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially…
In this work, we show existence of invariant ergodic measure for switched linear dynamical systems (SLDSs) under a norm-stability assumption of system dynamics in some unbounded subset of $\mathbb{R}^{n}$. Consequently, given a stationary…
We present a general theory of series-parallel mental architectures with selectively influenced stochastically non-independent components. A mental architecture is a hypothetical network of processes aimed at performing a task, of which we…