Related papers: Information Physics: The New Frontier
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
During the past three decades investigators have unveiled a number of deep connections between physical information and black holes whose consequences for ordinary systems go beyond what has been deduced purely from the axioms of…
Information theory, though originally developed for communications engineering, provides mathematical tools with broad applications across science. These tools characterize the fundamental limits of data compression and transmission in the…
In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
A colloquial interpretation of entropy is that it is the knowledge gained upon learning the outcome of a random experiment. Conditional entropy is then interpreted as the knowledge gained upon learning the outcome of one random experiment…
Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
This paper introduces several fundamental concepts in information theory from the perspective of their origins in engineering. Understanding such concepts is important in neuroscience for two reasons. Simply applying formulae from…
Information field theory (IFT) is the application of probabilistic reasoning to fields. Physical fields are mathematical functions over continuous spaces that exhibit certain properties of regularity, such as limited variance and finite…
Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their…
We review some recent advances in black hole thermodynamics, including statistical mechanical origins of black hole entropy and its leading order corrections, from the viewpoints of various quantum gravity theories. We then examine the…
A message of any sort can be regarded as a source of information. Claude. E. Shannon showed in the last century that information ("what we don't already know") is equivalent to the entropy as defined in statistical mechanics. A string of…
Information theory plays a central role in establishing fundamental limits on what any learning or estimation algorithm can -- and cannot -- achieve, regardless of computational power. In this chapter, we provide an introduction to these…
The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…
The experience from Quantum Information has lead us to look at Quantum Theory (QT) and the whole Physics from a different angle. The information-theoretical paradigm---"It from Bit'---prophesied by John Archibald Wheeler is relentlessly…
Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
Recent theoretical progress in nonequilibrium thermodynamics, linking the physical principle of Maximum Entropy Production ("MEP") to the information-theoretical "MaxEnt" principle of scientific inference, together with conjectures from…