Related papers: Information mechanics: conservation and exchange
I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More…
We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and…
The Price equation shows the unity between the fundamental expressions of change in biology, in information and entropy descriptions of populations, and in aspects of thermodynamics. The Price equation partitions the change in the average…
This paper consists of two parts. In the first part, we develop a new information theory, in which it is not a coincidence that information and physical entropy share the same mathematical formula. It is an adaptation of mind to help search…
Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of…
Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
Integrated information theory (IIT) is a theoretical framework that provides a quantitative measure to estimate when a physical system is conscious, its degree of consciousness, and the complexity of the qualia space that the system is…
Thermodynamics and information have intricate inter-relations. The justification of the fact that information is physical, is done by inter-linking information and thermodynamics - through Landauer's principle. This modern approach towards…
The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules…
In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…
Persuasion is the process of changing an agent's belief distribution from a given (or estimated) prior to a desired posterior. A common assumption in the acceptance of information or misinformation as fact is that the (mis)information must…
Thermodynamics establishes that information acquired through measurement can be converted into work, as exemplified by Maxwell's demon and Szilard engines. Most experimental realizations of information engines, however, implicitly assume…
Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…
Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…
The trade-off between the information gain and the state disturbance is derived for quantum operations on a single qubit prepared in a uniformly distributed pure state. The derivation is valid for a class of measures quantifying the state…
We show that the nonlocal Fisher information - defined as the entropy dissipation of the Boltzmann entropy for nonlocal heat equations - admits a natural lifting in the sense of Guillen and Silvestre (2025). Important examples include the…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical r\^{o}le…
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…