Related papers: Entropy of nonautonomous dynamical systems
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…
Entropy is arguably one of the most powerful concepts to understand the world, from the behavior of molecules to the expansion of the universe, from how life emerges to how hybrid complex systems like cities come into being and continue…
We consider two types of dynamical systems namely non-autonomous discrete dynamical systems(NDDS) and generic dynamical systems(GDS). In both of them, we study various notions of transitivity. We give many equivalent conditions for each of…
Let $\boldsymbol{X}=\{X_{k}\}_{k=0}^{\infty}$ be a sequence of compact metric spaces $X_{k}$ and $\boldsymbol{T}=\{T_{k}\}_{k=0}^{\infty}$ a sequence of continuous mappings $T_{k}:X_{k} \to X_{k+1}$. The pair…
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…
We overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on a set…
We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
We have shown how the intrinsic properties of a noise process can set an upper bound for the time derivative of entropy in a nonequilibrium system. The interplay of dissipation and the properties of noise processes driving the dynamical…
The problem of estimating entropy production from incomplete information in stochastic thermodynamics is essential for theory and experiments. Whereas a considerable amount of work has been done on this topic, arguably, most of it is…
A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…
We study questions motivated by results in the classical theory of dynamical systems in the context of triangulated and A-infinity categories. First, entropy is defined for exact endofunctors and computed in a variety of examples. In…
This paper is a non-technical, informal presentation of our theory of the second law of thermodynamics as a law that is independent of statistical mechanics and that is derivable solely from certain simple assumptions about adiabatic…
Entropy serves as a central observable in equilibrium thermodynamics. However, many biological and ecological systems operate far from thermal equilibrium. Here we show that entropy production can characterize the behavior of such…