Related papers: Induced topological pressure for countable state M…
We study discrete flow equivalence of two-sided topological Markov shifts by using extended Ruelle algebras. We characterize flow equivalence of two-sided topological Markov shifts in terms of conjugacy of certain actions weighted by…
In the context of geodesic flows of noncompact negatively curved manifolds, we propose three different definitions of entropy and pressure at infinity, through growth of periodic orbits, critical exponents of Poincar\'e series, and entropy…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
Let $X$ be a compact metric space and $\Phi=\{\varphi_t\}_{t\in\mathbb{R}}$ be a continuous flow on $X$. We introduce two types of topological pressure for family of discontinuous potentials $a=\{a_t\}_{t>0}$. First, define the topological…
We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional "layer-unique" Gibbs measures for which the same results can…
Stochastic thermodynamics provides the framework to analyze thermodynamic laws and quantities along individual trajectories of small but fully observable systems. If the observable level fails to capture all relevant degrees of freedom,…
We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently is generalized to the dynamics…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
A Polish group $G$ has the generic point property if any minimal $G$-flow admits a comeager orbit, or equivalently if the universal minimal flow (UMF) does. The class $\mathsf{GPP}$ of such Polish groups is a proper extension of the class…
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 define the projected entropy S(T) at a given temperature T in the context of an Ising model transition matrix calculation as the entropy associated with the distribution of Markov chain realizations in energy-magnetization, E-H, space.…
We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the…
Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
We want to relate the concepts of entropy and pressure to that of KMS states for $C^*$-Algebras. Several different definitions of entropy are known in our days. The one we describe here is quite natural and extends the usual one for…
We give a sufficient condition for a symbolic topological dynamical system with action of a countable amenable group to be an extension of the full shift, a problem analogous to those studied by Ashley, Marcus, Johnson and others for…
This paper compiles several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability…
In this paper, we consider a Borel measurable map of a compact metric space which admits an inducing scheme. Under the finite weighted complexity condition, we establish a thermodynamic formalism for a parameter family of potentials…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…