Related papers: Question on Conditional Entropy
The universe is certainly not yet in total thermodynamical equilibrium,so clearly some law telling about special initial conditions is needed. A universe or a system imposed to behave periodically gets thereby required ``initial…
We introduce an axiomatic approach for characterizing quantum conditional entropy. Our approach relies on two physically motivated axioms: monotonicity under conditional majorization and additivity. We show that these two axioms provide…
We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction…
Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case corrections to an (approximate)…
We show that the principle of entropy increase may be exactly founded on a few axioms valid not only for quantum and classical statistics, but also for a wide range of statistical processes.
From a new rigorous formulation of the general axiomatic foundations of thermodynamics we derive an operational definition of entropy that responds to the emergent need in many technological frameworks to understand and deploy thermodynamic…
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…
In this paper relations among some kinds of cumulative entropies and moments of order statistics are presented. By using some characterizations and the symmetry of a non negative and absolutely continuous random variable X, lower and upper…
Firstly, we calculate quantitatively decrease of entropy by the known formulas in the ordering phenomena and nucleation of thermodynamics of microstructure. They show again that a necessary condition of decrease of entropy in isolated…
Probably not, because there are lots of manifestly unanthropic ways of producing entropy. We demonstrate that the Causal Entropic Principle (CEP), as a replacement for the anthropic principle to explain the properties of the observed…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
Qubit Models which aim to resolve the information paradox must not redefine entanglement entropy as a redefinition does not address the correct issue of the information paradox. The purpose of this letter is to understand why any…
It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…
The total entropy production fluctuations are studied in some exactly solvable models. For these systems, the detailed fluctuation theorem holds even in the transient state, provided initially the system is prepared in thermal equilibrium.…
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…