Related papers: Critical Phenomena for Systems under Constraint

A wide variety of complex systems exhibit large fluctuations both in space and time that often can be attributed to the presence of some kind of critical phenomena. Under such critical scenario it is well known that the properties of the…

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…

This paper proposes that the mathematical relationship between an entropy distribution and its limit offers some new insight into system performance. This relationship is used to quantify variation among the entities of a system, where…

Experimental systems with a first order phase transition will often exhibit hysteresis when out of equilibrium. If defects are present, the hysteresis loop can have different shapes: with small disorder the hysteresis loop has a macroscopic…

Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…

When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This article reviews the general theory of such temporal fluctuations. We first survey some results on the…

There are several examples which show that the critical exponents can be dependent on initial condition of the system. In such situations, there are many systems where various issues related to the universal behavior e.g. existence of…

Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…

Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We consider three generalizations of contraction with…

The work performed on a system in a microcanonical state by changes in a control parameter is characterized in terms of its statistics. The transition probabilities between eigenstates of the system Hamiltonians at the beginning and the end…

The sensitive dependence of chaos on parameters is a topic of great interest in the study of integrability and stability of dynamical systems. Previous work has proposed ways to identify the sensitive dependence on parameters by topological…

This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…

We study decoherence induced by a dynamic environment undergoing a quantum phase transition. Environment's susceptibility to perturbations - and, consequently, efficiency of decoherence - is amplified near a critical point. Over and above…

We provide deterministic controllability conditions that imply exponential mixing properties for randomly forced constrained dynamical systems with possibly unbounded state space. As an application, new ergodicity results are obtained for…

The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the…

The characteristic function for the joint measurement of the changes of two commuting observables upon an external forcing of a quantum system is derived. In particular, the statistics of the internal energy, the exchanged heat and the work…

We consider the long-time behavior of systems close to a system with a smooth first integral. Under certain assumptions, the limiting behavior, to some extent, turns out to be universal: it is determined by the first integral, the…

We consider the effect of parametric uncertainty on properties of Linear Time Invariant systems. Traditional approaches to this problem determine the worst-case gains of the system over the uncertainty set. Whilst such approaches are…

While fields like Artificial Life have made huge strides in quantifying the mechanisms that distinguish living systems from non-living ones, particular mechanisms remain difficult to reproduce in silico. Known as open-endedness, we've been…

With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…