Related papers: Entropy driven transformations of statistical hype…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
The Gibbs sampler (a.k.a. Glauber dynamics and heat-bath algorithm) is a popular Markov Chain Monte Carlo algorithm which iteratively samples from the conditional distributions of a probability measure $\pi$ of interest. Under the…
Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium…
In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic…
In this paper we develop a global correspondence between immersed horospherically convex hypersurfaces in hyperbolic space and complete conformal metrics on domains in the sphere. We establish results on when the hyperbolic Gauss map is…
One of the few accepted dynamical foundations of non-additive "non-extensive") statistical mechanics is that the choice of the appropriate entropy functional describing a system with many degrees of freedom should reflect the rate of growth…
Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
In this paper we elaborate on the recently proposed superstatistics formalism [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)], used to interpret unconventional statistics. Their interpretation is that unconventional statistics in…
The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…
The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We…
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
We provide a quantum statistical basis for (a)a characterisation of a complete set of thermodynamic variables and (b) the differentiability of the entropy function of these variables
Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic…
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
Dynamical systems generated by $d\ge2$ commuting homeomorphisms (topological $\mathbb{Z}^d$-actions) contain within them structures on many scales, and in particular contain many actions of $\mathbb{Z}^k$ for $1\le k\le d$. Familiar…
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…