Related papers: Categorical polynomial entropy
This survey is dedicated to a new direction in the theory of dynamical systems: the dynamics of metrics in measure spaces and new (catalytic) invariants of transformations with invariant measure. A space equipped with a measure and a metric…
We examine the {combinatorial} or {probabilistic} definition ("Boltzmann's principle") of the entropy or cross-entropy function $H \propto \ln \mathbb{W}$ or $D \propto - \ln \mathbb{P}$, where $\mathbb{W}$ is the statistical weight and…
Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in…
The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each…
We give an autoequivalence of the derived category of the Ginzburg dg algebra for a mutation loop satisfying the sign stability introduced in [IK21]. We compute the categorical entropies of their restrictions to some subcategories and…
Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees…
There is a class of higher derivative gravity theories that are in some sense natural extensions of cosmological Einstein's gravity with a unique maximally symmetric classical vacuum and only a massless spin-2 excitation about the vacuum…
Stable homotopy theory is governed by the principle that after inverting loop spaces, homotopy types become the representing objects for homology theories. We show that this principle extends to higher category theory: inverting…
We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…
We present a unifying approach to the study of entropies in Mathematics, such as measure entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account discrete dynamical systems, that is, pairs $(X,T)$, where…
Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail…
We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, epsilon-entropy and topological entropy per unit time and volume have been introduced previously. In this…
We investigate the concept of definable, or inner, automorphism in the logical setting of partial Horn theories. The central technical result extends a syntactical characterization of the group of such automorphisms (called the covariant…
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving…
Inspired by Katok's intermediate entropy property [Inst. Hautes \'Etudes Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-time and continuous-time dynamical systems. By using…
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to investigate the topological properties of these operations between…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
We provide a multiplicative classification of polynomial endofunctors on spectra in terms of their Mackey functors of cross--effects. More precisely, we prove that various categories of multivariable excisive functors from spectra to…
We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and…