Related papers: A partial ordering of sets, making mean entropy mo…

After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure…

The probability distribution of the total entropy production in the non-equilibrium steady state follows a symmetry relation called the fluctuation theorem. When a certain part of the system is masked or hidden, it is difficult to infer the…

We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where…

The electronic structure of heavy elements, when described in a space-time which the metric is affected by the electromagnetic interaction, presents instabilities. These instabilities increase with the atomic number, and above a critical…

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…

Nature's many complex systems--physical, biological, and cultural--are islands of low-entropy order within increasingly disordered seas of surrounding, high-entropy chaos. Energy is a principal facilitator of the rising complexity of all…

The information processing capacity of a complex dynamical system is reflected in the partitioning of its state space into disjoint basins of attraction, with state trajectories in each basin flowing towards their corresponding attractor.…

Shannon's information entropy measures of the uncertainty of an event's outcome. If learning about a system reflects a decrease in uncertainty, then a plausible intuition is that learning should be accompanied by a decrease in the entropy…

It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…

We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…

A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…

We give the basic definition of algebraic entropy for lattice equations. The entropy is a canonical measure of the complexity of the dynamics they define. Its vanishing is a signal of integrability, and can be used as a powerful…

The differing ability of polypeptide conformations to act as the native state of proteins has long been rationalized in terms of differing kinetic accessibility or thermodynamic stability. Building on the successful applications of physical…

The aim of this paper is to use large deviation theory in order to compute the entropy of macrostates for the microcanonical measure of the shallow water system. The main prediction of this full statistical mechanics computation is the…

Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing…

The von Neumann entropy and the subentropy of a mixed quantum state are upper and lower bounds, respectively, on the accessible information of any ensemble consistent with the given mixed state. Here we define and investigate a set of…

Establishing an universal method to measure the organization of an universal system, will allow us to understand the mechanisms of functioning and organizing in general and enable us to design systems which will posses highest level of…

Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called ``caloric'') in transformations that are not isochoric (i.e.…

General hyperbolic systems of balance laws with inhomogeneity in space and time in all constitutive functions are studied in the context of relative entropy. A framework is developed in this setting that contributes to a measure-valued weak…

In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This…