Related papers: Systems with Almost Specification Property May Hav…
We demonstrate an intuitive relation between conditional entropy and conditional expectation that is useful when one want to compare them as measurement tools to evaluate secrecy systems. In particular, we give a Security Property…
We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic…
Let $(X,T)$ be a compact dynamical system. This article proves that if $(X,T)$ has the partial specification property, then it has the average shadowing property. It is also proven that if $(X,T)$ is surjective and has the partial…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
The problems of conditional entropy's definition and the formula to compute conditional entropy are analyzed from various perspectives, and the corrected computing formula is presented. Examples are given to prove the conclusion that…
The possibility that a short-range interacting system exhibits nonadditivity is investigated. After the discussion on the precise definition of additivity and its consequence, we show that it is possible when the system is in a…
It is known that the equilibrium properties of open classical systems that are strongly coupled to a heat bath are described by a set of thermodynamic potentials related to the system's Hamiltonian of mean force. By adapting this framework…
A notion of entropy is introduced for causal fermion systems. This entropy is a measure of the state of disorder of a causal fermion system at a given time compared to the vacuum. The definition is given both in the finite and…
In this paper, we establish sufficient conditions for the existence of error bounds at infinity for lower semicontinuous inequality systems. We also show that the existence of an error bound at infinity of constraint systems plays an…
The conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional…
An almost Einstein manifold satisfies equations which are a slight weakening of the Einstein equations; Einstein metrics, Poincare-Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are…
When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
We show that the typical dynamical system sometimes begins to behave like a non-deterministic system with a small classical entropy, and this behavior lasts an extremely long time, until the system starts decreasing entropy. Then again it…
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…
A colloquial interpretation of entropy is that it is the knowledge gained upon learning the outcome of a random experiment. Conditional entropy is then interpreted as the knowledge gained upon learning the outcome of one random experiment…
We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving…
The third law of thermodynamics dictates that the entropy of materials becomes zero as temperature ($T$) approaches zero. Contrarily, glass and other similar materials exhibit nonzero entropy at $T=0$, which contradicts the third law. For…
We study the complexity of deciding the equality of infinite objects specified by systems of equations, and of infinite objects specified by lambda-terms. For equational specifications there are several natural notions of equality: equality…
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 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…