Related papers: Does macroscopic disorder imply microscopic chaos?
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
The irreversibility in a statistical system is traced to its probabilistic evolution, and the molecular chaos assumption is not its unique consequence as is commonly believed. Under the assumption that the rate of change of the each…
According to the standard model of cosmology, the arrangement of matter in the cosmos on scales much larger than galaxies is entirely specified by the initial conditions laid down during inflation. But zooming in by dozens of orders of…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
General relativity exhibits a unique feature not represented in standard examples of chaotic systems; it is a spacetime diffeomorphism invariant theory. Thus many characterizations of chaos do not work. It is therefore necessary to develop…
Based on newly discovered properties of the shift map (Theorem 1), we believe that chaos should involve not only nearby points can diverge apart but also faraway points can get close to each other. Therefore, we propose to call a continuous…
A recent experiment on Brownian motion has been interpreted to exhibit direct evidence for microscopic chaos. In this note we demonstrate that virtually identical results can be obtained numerically using a manifestly microscopically…
Complexity is a measure of information content. Crystalline materials are not complex systems because their structures can be represented tersely using the language of crystallography. Disordered materials are also structurally simple if…
In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random fields is expected to…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
We provide a brief survey of quantum statistical characterisations of order, disorder and coherence in systems of many degrees of freedom. Here, order and coherence are described in terms of symmetry breakdown, while disorder is described…
An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
We reveal that realistic fluids generate microscopic-level discontinuity constantly and the discontinuity spreads out with motion of particles rather rapidly and widely. These things cannot be treated by the standard kinetic equations, and…
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic…
The notion of Bohr chaos was introduced in [3, 4]. We answer a question raised in [3] of whether a non uniquely ergodic minimal system of positive topological entropy can be Bohr chaotic. We also prove that all systems with the…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…
We give necessary and sufficient conditions for a hyperbolic set to be non-chaotic (or, conversely, chaotic) in a certain sense.
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase…