相关论文: A note about entropy

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…

Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…

In order to undestand how the complex concept of entropy emerged,we propose a trip towards the past reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since the Gibbs's work is not very well known, we present a…

Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle…

The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…

Transfer entropy is used to establish a measure of causal relationships between two variables. Symbolic transfer entropy, as an estimation method for transfer entropy, is widely applied due to its robustness against non-stationarity. This…

Shannon entropy is widely used to quantify the uncertainty of discrete random variables. But when normalized to the unit interval, as is often done in practice, it no longer conveys the alphabet sizes of the random variables being studied.…

The reasons for introducing the concept of the entrostat in statistical physics are examined. The introduction of the concept of the entrostat has allowed to show the possibility of self-organization in open systems within the understanding…

In this paper, the concept of L-algebra is revisited and after that, the article is prepared to deal with the notion of the entropy of an L-algebra. If a set has an L-algebraic structure, it is possible to calculate the degree of…

Entropy is critically examined as a fundamental concept in contemporary science and informatics. Although the typical Shannon entropy provides a proper framework for describing the canonical ensemble, it fails to represent adequately the…

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…

For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

*First-principles derivation of the entropy production in erectric static conduction. *The second-order (symmetric) density matrix contributes to the entropy production. *New schemes of steady states formulated using a relaxation-type von…

These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…