Related papers: Entropy of nonautonomous dynamical systems
Even today, the concept of entropy is perceived by many as quite obscure. The main difficulty is analyzed as being fundamentally due to the subjectivity and anthropocentrism of the concept that prevent us to have a sufficient distance to…
We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.
The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…
In this paper, we investigate and compare two well-developed definitions of entropy relevant for describing the dynamics of isolated quantum systems: bipartite entanglement entropy and observational entropy. In a model system of interacting…
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
We study the relations between the averaged linear entropy production in periodically measured quantum systems and ergodic properties of their classical counterparts. Quantized linear automorphisms of the torus, both classically chaotic and…
A notion of time is fundamental in the study of dynamical systems. Time arises as a standalone dynamical system and also in solutions or trajectories as a special kind of map between systems. We characterize time by a universal property and…
The entropy production rate is a key quantity in non-equilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress towards its full grasping. By…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
The paper is a survey of dynamical entropy of automorphisms of operator algebras. We describe the different entropies of Connes-Stormer, Connes-Narnhofer-Thirring, Sauvageot-Thouvenot, and Voiculescu, and discuss the main examples of the…
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…
Modes of physical fields which are located inside a horizon and which cannot be observed by a distant observer are identified with dynamical degrees of freedom of a black hole. A new invariant statistical mechanical definition of a…
Macroscopic nonextensive thermodynamics is studied without recourse to microscopic statistical mechanics. It is shown that if entropy is nonextensive, the concept of physical temperature introduced through the generalized zeroth law of…
Multiscale thermodynamics is a theory of relations among levels of description. Energy and entropy are its two main ingredients. Their roles in the time evolution describing approach of a level (starting level) to another level involving…
We do not attempt to provide yet another definition of selforganization, but explore the conditions under which we can model a system as self-organizing. These involve the dynamics of entropy, and the purpose, aspects, and description level…
In this paper, we focus on some properties, calculations and estimations of topological entropy for a nonautonomous dynamical system $(X,f_{0,\infty})$ generated by a sequence of continuous self-maps $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ on…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…