Related papers: Entropy formula of folding type for $C^{1+\alpha}$…
Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the…
Suppose f is a $C^{1+\alpha}$ surface diffeomorphism, and m is an equilibrium measure of a Holder continuous potential. We show that if m has positive metric entropy, then f is measure theoretically isomorphic to the product of a Bernoulli…
We present a general framework for deriving entropy production rates (EPRs) in active matter systems driven by non-Gaussian active fluctuations. Employing the probability-flow equivalence technique, we rigorously obtain an entropy…
The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…
Given a closed, oriented, compact surface $S$ of constant negative curvature and genus $g \ge 2$, we study the measure-theoretic entropy of the Bowen-Series boundary map with respect to its smooth invariant measure. We obtain an explicit…
Entropy and free-energy estimation are key in thermodynamic characterization of simulated systems ranging from spin models through polymers, colloids, protein structure, and drug-design. Current techniques suffer from being model specific,…
We construct the entropic measure $\mathbb{P}^\beta$ on compact manifolds of any dimension. It is defined as the push forward of the Dirichlet process (another random probability measure, well-known to exist on spaces of any dimension)…
We study a class of asymptotically entropy-expansive $C^1$ diffeomorphisms with dominated splitting on a compact manifold $M$, that satisfy the specification property. This class includes, in particular, transitive Anosov diffeomorphisms…
Entropy principles based on thermodynamic consistency requirements are widely used for constitutive modeling in continuum mechanics, providing physical constraints on a priori unknown constitutive functions. The well-known M\"uller-Liu…
For an ergodic hyperbolic measure $\omega$ of a $C^{1+{\alpha}}$ diffeomorphism, there is an $\omega$ full-measured set $\tilde\Lambda$ such that every nonempty, compact and connected subset $V$ of $\mathbb{M}_{inv}(\tilde\Lambda)$…
Suppose f is a C^{1+\epsilon} surface diffeomorphism with positive topological entropy. For every positive \delta strictly smaller than the topological entropy of f we construct an invariant Borel set E such that (a) f|E has a countable…
In this paper we study the geodesic flow for a particular class of Riemannian non-compact manifolds with variable pinched negative sectional curvature. For a sequence of invariant measures we are able to prove results relating the loss of…
We introduce the notion of tubular dimension, and give a formula for it. As an application we show that every invariant measure of a $C^{1+\gamma}$ diffeomorphism of a closed Riemannian manifold admits an asymptotic local product structure…
The entropy change of a (non-equilibrium) Markovian ensemble is calculated from (1) the ensemble phase density $p(t)$ evolved as iterative map, $p(t) = \mathbb{M}(t) p(t- \Delta t)$ under detail balanced transition matrix $\mathbb{M}(t)$,…
Given a general scalar balance law, i.e., in several space dimensions and with flux and source both space and time dependent, we focus on the functional properties of the entropy production. We apply this operator to entropy solutions, to…
For a given topological dynamical system $(X,T)$ over a compact set $X$ with a metric $d$, the "variational principle" states that \begin{equation*} \sup_{\mu}h_\mu(T) = h(T) = h_d(T), \end{equation*} where $h_\mu(T)$ is the…
We give a new type of sufficient condition for the existence of measures with maximal entropy for an interval map $f$, using some non-uniform hyperbolicity to compensate for a lack of smoothness of $f$. More precisely, if the topological…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
Pesin's identity provides a profound connection between entropy $h_{KS}$ (statistical mechanics) and the Lyapunov exponent $\lambda$ (chaos theory). It is well known that many systems exhibit sub-exponential separation of nearby…
We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…