Related papers: Is ergodicity a reasonable hypothesis?
Pugh and Shub have conjectured that essential accessibility implies ergodicity, for a $C^2$, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center bunching assumption, which is satsified by all…
We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover,…
For discrete-time Markov chains on general state spaces, we establish criteria for non-ergodicity and non-strong ergodicity, and derive sufficient conditions for non-geometric ergodicity via the theory of minimal nonnegative solutions. Our…
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…
We consider a time inhomogeneous strong Markov process $(\xi_t)_{t\ge 0}$ taking values in a Polish state space whose semigroup has a $T$-periodic structure. We give simple conditions which imply ergodicity of the grid chain…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
The second law of thermodynamics states that entropy production in macroscopic systems is non-negative, reaching zero only at thermodynamic equilibrium. As a corollary, this implies that the state trajectory of macroscopic systems is…
We consider a class of multi-layer interacting particle systems and characterize the set of ergodic measures with finite moments. The main technical tool is duality combined with successful coupling.
The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by…
This paper is a physicist's review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here we present a unified, graph-based view of all archetypical models of such universality (billiards,…
Ergodicity, the central tenet of statistical mechanics, requires that an isolated system will explore all of its available phase space permitted by energetic and symmetry constraints. Mechanisms for violating ergodicity are of great…
This letter raises the possibility that ergodicity concerns might have some bearing on the signal-to-noise paradox. This is explored by applying the ergodic theorem to the theory behind ensemble weather forecasting and the ensemble mean.…
Ergodicity is a fundamental issue for a stochastic process. In this paper, we refine results on ergodicity for a general type of Markov chain to a specific type or the $GI/G/1$-type Markov chain, which has many interesting and important…
Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective…
It is shown that if physical space time were truly compact there would only be of the order of one solutions to the classical field equations with a weighting to be explained. But that would not allow any peculiar choice of initial…
We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to equilibrium is exponential. This result is of interest…
The fact that we apparently live in an accelerating universe places limitations on where humans might visit. If the current energy density of the universe is dominated by a cosmological constant, a rocket could reach a galaxy observed today…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
The problem is discussed of whether a traveller can reach a remote object and return back sooner than a photon would when taken into account that the traveller can partly control the geometry of his world. It is argued that under some…
A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as…