相关论文: Entropy dissipation estimates in a Zero-Range dyna…

On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…

Motivated by the entropy computations relevant to the evaluation of decrease in entropy in bit reset operations, the authors investigate the deficit in an entropic inequality involving two independent random variables, one continuous and…

Properties of the max- relative entropy of entanglement are investigated, and its significance as an upper bound to the one shot rate for perfect entanglement dilution, under a particular class of quantum operations, is discussed. It is…

We show that the typical dynamical system sometimes begins to behave like a non-deterministic system with a small classical entropy, and this behavior lasts an extremely long time, until the system starts decreasing entropy. Then again it…

We study the energy flow of dissipative dynamics on infinite lattices, allowing the total energy to be infinite and considering formally gradient dynamics. We show that in spatial dimensions 1,2, the flow is for almost all times arbitrarily…

Explicit expressions for arrival times of particles moving in a one-dimensional Zero-Range Process (ZRP) are computed. Particles are fed into the ZRP from an injection site and can also evaporate from anywhere in the interior of the ZRP.…

In earlier works, we have shown the uniform decay of the local energy of the damped wave equation in exterior domain when the damper is spatially localized near captive rays. In order to have uniform decay of the total energy, the damper…

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns…

We study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.

Zero-range processes with decreasing jump rates exhibit a condensation transition, where a positive fraction of all particles condenses on a single lattice site when the total density exceeds a critical value. We study the onset of…

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…

Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…

The quantum thermodynamic property of the fractional damping system is investigated extensively. A fractional power-law decaying entropy function is revealed which presents another evidence for the validity of the third law of…

A model to explain the statistics of the velocity gradients in the dissipation range of a turbulent flow is presented. The experimentally observed non-gaussian statistics is theoretically predicted by means of a thermodynamical analogy…

We consider exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the…

We present a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow,…

In this paper, we study the large--time behavior of a numerical scheme discretizing drift-- diffusion systems for semiconductors. The numerical method is finite volume in space, implicit in time, and the numerical fluxes are a…

In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at…

We discuss the microscopic definition of entropy production rate in a model of a dissipative system: a sheared fluid in which the kinetic energy is kept constant via a Gaussian thermostat. The total phase space contraction rate is the sum…

The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…