Related papers: A short note on basic of information geometry from…
This Colloquium is a fast journey through the build-up of key thermodynamical concepts, i.e. work, heat and irreversibility -- and how they relate to information. Born at the time of industrial revolution to optimize the exploitation of…
This set of notes is intended for a short course aiming to provide an (almost) self-contained and (almost) elementary introduction to the topic of Information Geometry (IG) of the probability simplex. Such a course can be considered an…
The goal of this paper is to present a general thermodynamic basis that is useable in the context of superconductivity and particle accelerators. The first part recalls the purpose of thermodynamics and summarizes its important concepts.…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
We find the information geometry of tempered stable processes. Beginning with the derivation of $\alpha$-divergence between two tempered stable processes, we obtain the corresponding Fisher information matrices and the $\alpha$-connections…
This book provides an introduction to the emerging field of quantum thermodynamics, with particular focus on its relation to quantum information and its implications for quantum computers and next generation quantum technologies. The text,…
We develop an axiomatic reconstruction of thermodynamics based entirely on two primitive components: a description of what aspects of a system are observed and a reference measure that encodes the underlying descriptive convention. These…
This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of…
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,…
Thermodynamics is a macroscopic physical theory whose two very general laws are independent of any underlying dynamical laws and structures. Nevertheless, its generality enables us to understand a broad spectrum of phenomena in physics,…
The basic idea of a microscopic understanding of Thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities's semi-classical…
The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of…
We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, $\alpha$-connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
Thought experiments involving thermodynamic principles have often been used to derive fundamental physical limits to information processing and storage. Similar thought experiments involving black holes can shed further light into such…
We can incorporate a "time" evolution into thermodynamics as a Hamilton-Jacobi dynamics. A set of the equations of states in thermodynamics is considered as the generalized eikonal equation, which is equivalent to Hamilton-Jacobi equation.…
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…
This paper presents a comprehensive review of geometrical thermodynamics, which employs geometric concepts to study the thermodynamic properties of physical systems. The review covers key topics such as thermodynamic fluctuation theory,…
These condensed notes treat some basic notions in Tropical Geometry (varieties, cycles, modifications, equivalence). These topics are to be extended, illustrated and included to the upcoming book project…
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…