相关论文: The Poincar\'e-Boltzmann Machine: from Statistical…
We introduce a constructive framework for assigning thermodynamic structure to an arbitrary data system from its measured microstates. Starting from an empirical distribution over configurations, we first infer a data-driven energy function…
What does the informational complexity of dynamical networked systems tell us about intrinsic mechanisms and functions of these complex systems? Recent complexity measures such as integrated information have sought to operationalize this…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
We introduce \emph{Information Topology}: a framework that unifies information theory and algebraic topology by treating \emph{cycle closure} as the primitive operation of inference. The starting point is the \emph{dot-cycle dichotomy},…
Information has intrinsic geometric and topological structure, arising from relative relationships beyond absolute values or types. For instance, the fact that two people share a meal describes a relationship independent of the meal's…
In recent years, the application of machine learning to physics has been actively explored. In this paper, we study a method for estimating the ground-state energy of quantum Hamiltonians by applying data-driven Koopman analysis within the…
Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…
This paper revisits Brownian motion from the perspective of Information Theory, aiming to explore the connections between Information Theory, Thermodynamics, and Complex Science. First, we propose a single-particle discrete Brownian motion…
We suggest that holography can be formulated in terms of the information capacity of the St\"uckelberg degrees of freedom that maintain gauge invariance of the theory in the presence of an information boundary. These St\"uckelbergs act as…
Part 1 has studied the conversion of observed random process with its hidden information to related dynamic process, applying entropy functional measure (EF) of the random process and path functional information measure (IPF) of the dynamic…
We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot statements of the second law of thermodynamics, for situations involving information processing. To this end, we consider an information reservoir (representing, e.g. a…
In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
This thesis investigates the interactions of different degrees of freedom of one joint system within the theory of stochastic thermodynamics. First, a comprehensive introduction to the subjects of stochastic processes, information theory…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
A kinetic approach to the notion of information is proposed, based on Liouville kinetic theory. The general kinetic equation for the evolution of the N-particle information $\mathcal{I}_N$ in a Hamiltonian system of large particle number…
We propose a geometric theory of non-equilibrium thermodynamics, namely geometric thermodynamics, using our recent developments of differential-geometric aspects of entropy production rate in non-equilibrium thermodynamics. By revisiting…