Related papers: Studies of entropy measures concerning the gaps of…
Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established…
The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…
In this paper, a method of measuring the entropy is presented. Problems related to the entropy and the heat are also discussed.
Whereas for strings, higher-order empirical entropy is the standard entropy measure, several different notions of empirical entropy for trees have been proposed in the past, notably label entropy, degree entropy, conditional versions of the…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Using periodic points we study a notion of entropy with values in the p-adic numbers. This is done for actions of countable discrete residually finite groups $\Gamma$. For suitable $\Gamma = \mathbb{Z}^d$-actions we obtain p-adic analogues…
Given any finite set equipped with a probability measure, one may compute its Shannon entropy or information content. The entropy becomes the logarithm of the cardinality of the set when the uniform probability is used. Leinster introduced…
The entropy of the random walk on the discrete contable group could be used for comparison of the system of the generators. Fundamental inequality between growth, entropy and escape gives the possibility to define "the best" system of the…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
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…
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…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
A Massey-like inequality is any useful lower bound on guessing entropy in terms of the computationally scalable Shannon entropy. The asymptotically optimal Massey-like inequality is determined and further refined for finite-support…
How does the information flow between different brain regions during various stimuli? This is the question we aim to address by studying complex cognitive paradigms in terms of Information Theory. To assess creativity and the emergence of…
Beyond the local constraints imposed by grammar, words concatenated in long sequences carrying a complex message show statistical regularities that may reflect their linguistic role in the message. In this paper, we perform a systematic…
When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility…
The diversity of a community that cannot be fully counted must be inferred. The two preeminent inference methods are the MaxEnt method, which uses information in the form of constraints and Bayes' rule which uses information in the form of…
We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy…