Related papers: Follower, Predecessor, and Extender Entropies
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic…
In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any…
The pattern of isentropes in the vicinity of a first-order phase transition is proposed as a key for a sub-classification. While the confinement--deconfinement transition, conjectured to set in beyond a critical end point in the QCD phase…
Accelerating mirrors provide a simple conceptual laboratory for studying particle production and the relation between trajectory and particle, energy, and entropy fluxes. We focus on the relation between energy and entropy, studying some…
In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are…
We study the entanglement entropy of a scalar filed in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. In both models we evaluate numerically the resulting entropies and find that they are proportional to the number…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform…
We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…
A {\it uniformly $p$-to-one endomorphism} is a measure-preserving map with entropy log $p$ which is almost everywhere $p$-to-one and for which the conditional expectation of each preimage is precisely $1/p$. The {\it standard} example of…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
We use a simple hard-core gas model to study the dynamics of small exploding systems. The system is initially prepared in a thermalized state in a spherical container and then allowed to expand freely into the vacuum. We follow the…
We show that minimal shifts with zero topological entropy are topologically conjugate to interval exchange transformations, generally infinite. When these shifts have linear factor complexity (linear block growth), the conjugate interval…
Epistasis is a key concept in the theory of adaptation. Indicators of epistasis are of interest for large system where systematic fitness measurements may not be possible. Some recent approaches depend on information theory. We show that…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
We show that non-perturbative entities such as solitons and instantons saturate bounds on entropy when the theory saturates unitarity. Simultaneously, the entropy becomes equal to the area of the soliton/instanton. This is strikingly…
The new notion of adjoint algebraic entropy of endomorphisms of Abelian groups is introduced. Various examples and basic properties are provided. It is proved that the adjoint algebraic entropy of an endomorphism equals the algebraic…
We establish a general criterion on the upper semi-continuity of partial entropy in all directions for $C^{1+\alpha}$ diffeomorphisms: it holds when the respective sums of Lyapunov exponents are continuous. This addresses, in arbitrary…
We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…