相关论文: Information geometry and Frobenius algebra
We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as…
A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of Yang-Mills gauge theories without making…
We propose a fundamental duality between the geometric properties of spacetime and the informational content of quantum fields. Specifically, we establish that the curvature of spacetime is directly related to the entanglement entropy of…
The significance of statistical physics concepts such as entropy extends far beyond classical thermodynamics. We interpret the similarity between partitions in statistical mechanics and partitions in Bayesian inference as an articulation of…
Information (I) is defined as the amount of the data after data compression. The first law of information theory: the total amount of data L (the sum of entropy S and information I) of an isolated system remains unchanged. The second law of…
This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing statistical independencies, mediated by Markov blankets, speak to a recursive composition of ensembles (of…
We formulate a bi-Connection Theory of Gravity whose Gravitational action consists of a recently defined mutual curvature scalar. Namely, we build a gravitational theory consisting of one metric and two affine connections, in a…
We argue that, when coupled to Einstein's theory of gravity, the Yukawa theory may solve the cosmological constant problem in the following sense: The radiative corrections of fermions generate an effective potential for the scalar field,…
We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
Recently, it has been shown that the statistical manifold, related to exponential families, has a Frobenius manifold structure and appears as the fourth class of Frobenius manifolds. It has a structure of a projective manifold over a rank…
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces,…
We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can…
We construct an information-geometric structure for chemical thermodynamics, applicable to a wide range of chemical reaction systems including non-ideal and open systems. For this purpose, we explicitly construct dual affine coordinate…
A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. As the main approximation the self-consistent field model is chosen, which allows in a certain degree to account for…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
We study the statistical monotonicity of the scalar curvature for the alpha-geometries on the simplex of probability vectors. From the results obtained and from numerical data we are led to some conjectures about quantum alpha-geometries…
The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in…