Related papers: Emergence time, curvature, space, causality, and c…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
Complexity matching characterizes the role of information in interactions between systems and can be traced back to the 1957 Introduction to Cybernetics by Ross Ashby. We argue that complexity can be expressed in terms of crucial events,…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown…
A core feature of complex systems is that the interactions between elements in the present causally constrain each-other as the system evolves through time. To fully model all of these interactions (between elements, as well as ensembles of…
The information shared among observables representing processes of interest is traditionally evaluated in terms of macroscale measures characterizing aggregate properties of the underlying processes and their interactions. Traditional…
Pairwise interactions between individuals are taken as fundamental drivers of collective behavior responsible for group cohesion and decision-making. While an individual directly influences only a few neighbors, over time indirect…
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…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
To infer information flow in any network of agents, it is important first and foremost to establish causal temporal relations between the nodes. Practical and automated methods that can infer causality are difficult to find, and the subject…
In closed quantum many-body systems, initially localized information spreads throughout the system and becomes highly complex. This phenomenon, known as information scrambling, is closely related to entropy growth and quantum…
Complex high-dimensional co-occurrence data are increasingly popular from a complex system of interacting physical, biological and social processes in discretely indexed modifiable areal units or continuously indexed locations of a study…
Orbital entropies, pair entropies, and mutual information have become popular tools for analysis of strongly correlated wave functions. They can quantitatively measure how strongly an orbital (e.g. from the DMRG active space) participates…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
The position and momentum space information entropies, of the ground state of the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These entropies for…
Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…
The use of coarse graining to connect physical and information theoretic entropies has recently been given a precise formulation in terms of ``observational entropy'', describing entropy for observers with respect to a measurement. Here we…
Humans are adept at uncovering abstract associations in the world around them, yet the underlying mechanisms remain poorly understood. Intuitively, learning the higher-order structure of statistical relationships should involve complex…
A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…