Related papers: Entropy of geometric structures
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
In any static spacetime the quasilocal Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics, and…
We introduce a natural nondegeneracy condition for Poisson structures, called holonomicity, which is closely related to the notion of a log symplectic form. Holonomic Poisson manifolds are privileged by the fact that their deformation…
We review a new form of entropy suggested by us, with origin in mixing of states of systems due to interactions and deformations of phase cells. It is demonstrated that this nonextensive form also leads to asymmetric maximal entropy…
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways…
We discuss a new simple field theory approach of Coulomb systems. Using a description in terms of fields, we introduce in a new way the statistical degrees of freedom in relation with the quantum mechanics. We show on a series of examples…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…
We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…
A class of two dimensional field theories, based on (generically degenerate) Poisson structures and generalizing gravity-Yang-Mills systems, is presented. Locally, the solutions of the classical equations of motion are given. A general…
We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
Sofic entropy is an invariant for probability-preserving actions of sofic groups. It was introduced a few years ago by Lewis Bowen, and shown to extend the classical Kolmogorov-Sinai entropy from the setting of amenable groups. Some parts…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's…
We show that linear inequalities for entropies have a natural geometric interpretation in terms of Hausdorff and packing dimensions, using the point-to-set principle and known results about inequalities for complexities, entropies and the…
Many Euclidean Einstein manifolds possess continuous symmetry groups of at least one parameter and we consider here a classification scheme of $d$ dimensional compact manifolds based on the existence of such a one parameter group in terms…