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A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
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…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…
The routine definitions of both entropy, and differential entropy show inconsistencies that make them not reciprocally coherent. We propose a few possible modifications of these quantities so that 1) they no longer show incongruities, 2)…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…
For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
Organisms and algorithms learn probability distributions from previous observations, either over evolutionary time or on the fly. In the absence of regularities, estimating the underlying distribution from data would require observing each…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
Evolution of a multiplicity distribution can be described with the help of master equation. We first look at 3rd and 4th factorial moments of multiplicity distributions and derive their equilibrium values. From them central moments and…
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…