Related papers: Entropy-driven cutoff phenomena
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…
The task of determining the origin of a drifting object after it has been located is highly complex due to the uncertainties in drift properties and environmental forcing (wind, waves and surface currents). Usually the origin is inferred by…
We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
The motion of a particle in a correlated random potential under the influence of a driving force is investigated in mean field theory. The correlations of the disorder are characterized by a short distance cutoff and a power law decay with…
This paper proposes and studies a detection technique for adversarial scenarios (dubbed deterministic detection). This technique provides an alternative detection methodology in case the usual stochastic methods are not applicable: this can…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the…
We study the random walk on a finite dihedral group $G$ driven by the uniform measure on $k$ independently and uniformly chosen elements. We show that the walk exhibits cutoff with high probability throughout nearly the entire regime $1 \ll…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class…
The structure of the network can be described by motifs, which are subgraphs that often repeat themselves. In order to understand the structure of network motifs, it is of great importance to study subgraphs from the perspective of…
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…
We show that a tight-binding one-dimensional chain composed of interacting and non-interacting atomic sites can exhibit multiple mobility edges at different values of carrier energy in presence of external electric field. Within a mean…
Consider a state of a system with several subsystems. The entropies of the reduced state on different subsystems obey certain inequalities, provided there is an equivalence relation, and a function measuring volumes or weights of…
Leakages are a major risk in water distribution networks as they cause water loss and increase contamination risks. Leakage detection is a difficult task due to the complex dynamics of water distribution networks. In particular, small…