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We investigate how to measure and define the entropy of a simple chaotic system, three hard spheres on a ring. A novel approach is presented, which does not assume the ergodic hypothesis. It consists of transforming the particles collision…
We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid…
The true process that generated data cannot be determined when multiple explanations are possible. Prediction requires a model of the probability that a process, chosen randomly from the set of candidate explanations, generates some future…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer…
Accurately determining dependency structure is critical to discovering a system's causal organization. We recently showed that the transfer entropy fails in a key aspect of this---measuring information flow---due to its conflation of dyadic…
The $\epsilon$-machine is a stochastic process' optimal model -- maximally predictive and minimal in size. It often happens that to optimally predict even simply-defined processes, probabilistic models -- including the $\epsilon$-machine --…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this…
Usually, it is supposed that irreversibility of time appears only in macrophysics. Here, we attempt to introduce the microphysical arrow of time assuming that at a fundamental level nature could be non-associative. Obtaining numerical…
Retrocausal models of QM add further weight to the conflict between causality and the possible existence of free will. We analyze a simple closed causal loop ensuing from the interaction between two systems with opposing thermodynamic time…
A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
For a system of two parties, the process matrix framework predicts the existence of causally nonseparable structures. We characterize the information exchanged, showing that the total entropy of the two parties acts as a measure for the…