Related papers: Systems with Almost Specification Property May Hav…
Many theoretical expressions of dissipation along non-equilibrium processes have been proposed. However, they have not been fully verified by experiments. Especially for systems strongly interacting with environments the connection between…
We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit…
We introduce a novel quantity for general dynamical systems, which we call the asymptotic uniform complexity. We prove an inequality relating the asymptotic uniform complexity of a dynamical system to its mean topological matching number.…
Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map with the specification property, and $\varphi: X \mapsto \IR$ a continuous function. We consider the set of points for which the Birkhoff average of $\varphi$ does…
Non-equilibrium and equilibrium thermodynamics of an interacting component in a special-relativistic multi-component system is discussed by use of an entropy identity. The special case of the corresponding free component is considered.…
We study one of the strongest versions of chaos for continuous dynamical systems, namely the specification property. We extend the definition of specification property for operators on a Banach space to strongly continuous one-parameter…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
We find a new formula for the limit of the capacity of certain sequences of multidimensional semiconstrained systems as the dimension tends to infinity. We do so by generalizing the notion of independence entropy, originally studied in the…
We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give…
In this paper we present a systematic study of shadowing properties with average error in tracing such as (asymptotic) average shadowing, $\underline{d}$-shadowing, $\overline{d}$-shadowing and almost specification. As the main tools we…
Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space(compactness and metrizability not necessarily required). This is achieved through the consideration of…
Answering Vershik's question we show that quasi-similarity does not conserve the entropy, proving quasi-similarity of all Bernoulli actions of a countable infinite group. We prove also the following generalization of Pinsker's theorem: the…
Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to…
In this article, we explore properties of pseudo entropy [1] in quantum field theories and spin systems from several approaches. Pseudo entropy is a generalization of entanglement entropy such that it depends on both an initial and final…
We establish an approximate zero-one law for sentences of continuous logic over finite metric spaces of diameter at most $1$. More precisely, we axiomatize a complete metric theory $T_{\mathrm{as}}$ such that, given any sentence $\sigma$ in…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
We delineate a methodology for the specification and verification of flow security properties expressible in the opacity framework. We propose a logic, OpacTL , for straightforwardly expressing such properties in systems that can be…
A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities.
It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect…