Related papers: Group structure as a foundation for entropies
In transformations between nonequilibrium stationary states, entropy might be a not well defined concept. It might be analogous to the ``heat content'' in transformations in equilibrium which is not well defined either, if they are not…
Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system's observed emergent patterns. Recent developments…
The entropy of a hierarchical network topology in an ensemble of sparse random networks with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble.We obtain a…
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…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
The entanglement of formation as well as the conditional entropy can be used to define leaves in the state space, given by a linear superposition of their extremal points. Examples are presented, where these leaves can be specified and can…
In statistical physics entropy is usually introduced as a global quantity which expresses the amount of information that would be needed to specify the microscopic configuration of a system. However, for lattice models with infinitely many…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…
The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and…
An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared…
We numerically determine the entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the…
Entropy production is a universal measure of irreversibility and energy dissipation in physical, chemical, and biological systems operating far from equilibrium. However, quantifying and spatiotemporally localising it in complex processes…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…
Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
A colloquial interpretation of entropy is that it is the knowledge gained upon learning the outcome of a random experiment. Conditional entropy is then interpreted as the knowledge gained upon learning the outcome of one random experiment…