相关论文: Entropies from coarse-graining: convex polytopes v…

We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on…

We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform…

We develop the framework of classical Observational entropy, which is a mathematically rigorous and precise framework for non-equilibrium thermodynamics, explicitly defined in terms of a set of observables. Observational entropy can be seen…

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…

This text studies, on the one hand, certain monotonicity properties of the Araki-Uhlmann relative entropy and, on the other hand, unbounded perturbation theory of KMS-states which facilitates a proof of the two-sided Bogoliubov inequality…

Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…

Euclidean path integrals for UV-completions of $d$-dimensional bulk quantum gravity were studied in [1] by assuming that they satisfy axioms of finiteness, reality, continuity, reflection-positivity, and factorization. Sectors ${\cal…

Generalizing the group structure of the Euclidean space, we construct a Riemannian metric on the deformed set \ $\mathbb{R}^n_q$ \ induced by the Tsallis entropy composition property. We show that the Tsallis entropy is a "hyperbolic…

On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation.…

In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popov's horospherical degenerations of complex algebraic varieties with the action of a complex linearly reductive group. We…

We attempt to find a function that characterizes gravitational clumping and that increases monotonically as inhomogeneity increases. We choose $S = ln\Omega$ as the candidate ``gravitational entropy'' function, where $\Omega$ is the…

We measure the entropy change of charge transitions in an electrostatically defined quantum dot in bilayer graphene. Entropy provides insights into the equilibrium thermodynamic properties of both ground and excited states beyond transport…

We consider the concept of generalized measure-theoretic entropy, where instead of the Shannon entropy function we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this…

Convexity properties of the entropy along displacement interpolations are crucial in the Lott-Sturm-Villani theory of lower bounded curvature of geodesic measure spaces. As discrete spaces fail to be geodesic, an alternate analogous theory…

Inspired by holographic Wilsonian renormalization, we consider coarse graining a quantum system divided between short distance and long distance degrees of freedom, coupled via the Hamiltonian. Observations using purely long distance…

In this paper, we explore the question of how different gauge choices in a gauge theory affect the tensor product structure of the Hilbert space in configuration space. In particular, we study the Coulomb gauge and observe that the naive…

The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…

In this paper we introduce a nonextensive quantum information theoretic measure which may be defined between any arbitrary number of density matrices, and we analyze its fundamental properties in the spectral graph-theoretic framework.…

Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…

We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena arXiv:1304.4926 have provided a method to derive the equations for the entangling surface from first principles. We use…