Related papers: Entropy dissipation estimates in a Zero-Range dyna…
We use a simple hard-core gas model to study the dynamics of small exploding systems. The system is initially prepared in a thermalized state in a spherical container and then allowed to expand freely into the vacuum. We follow the…
We study the approach to equilibrium of systems of gas particles in terms of relative entropy. The systems are modeled by the Kac master equation in arbitrary dimensions. First, we study the Kac system coupled to a thermostat, and secondly…
We study the geometric distribution of the relative entropy of a charged localised state in Quantum Field Theory. With respect to translations, the second derivative of the vacuum relative entropy is zero out of the charge localisation…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
Estimating the dissipation, or the entropy production rate (EPR), can provide insights into the underlying mechanisms of nonequilibrium driven processes. Experimentally, however, only partial information can be accessed, and the ability to…
The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and…
The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
A quantity of interest to characterise continuous-valued stochastic processes is the differential entropy rate. The rate of convergence of many properties of LRD processes is slower than might be expected, based on the intuition for…
The expressions for entropy production, free energy, and entropy extraction rates are derived for a Brownian particle that walks in an underdamped medium. Our analysis indicates that as long as the system is driven out of equilibrium, it…
Under a precise nonlinearity-diffusivity assumption we establish the decay of entropy solutions of a degenerate nonlinear parabolic equation with initial data being a sum of periodic function and a function vanishing at infinity (in the…
The steady-state distributions and dynamical behaviour of Zero Range Processes with hopping rates which are non-monotonic functions of the site occupation are studied. We consider two classes of non-monotonic hopping rates. The first…
In a glassy system different degrees of freedom have well-separated characteristic times, and are described by different temperatures. The stationary state is essentially non-equilibrium. A generalized statistical thermodynamics is…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
Active systems comprise a class of nonequilibrium dynamics in which individual components autonomously dissipate energy. Efforts towards understanding the role played by activity have centered on computation of the entropy production rate…
A classical approach for the analysis of the longtime behavior of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally $\Phi$-entropies. Via purely analytic arguments it can be shown that these…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
For Euclidean pure point diffractive Delone sets of finite local complexity and with uniform patch frequencies it is well known that the patch counting entropy computed along the closed centred balls is zero. We consider such sets in the…