Related papers: Information Theory of Action : Reconstructing Quan…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
From the output produced by a memoryless deletion channel with a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources…
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…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…
The relation between quantum theory and special relativity is peculiar. On the one hand it is close and essential. Steven Weinberg [1], for example, takes the position that the standard model is an inevitable consequence of the marriage of…
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
The model of the physical system with discrete interactions is based on the postulates that (i) parameters of the physical system are defined in process of its interaction; (ii) the process of interaction is discrete. Consequently ordering…
Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
The possibility is discussed of inferring or simulating some aspects of quantum dynamics by adding classical statistical fluctuations to classical mechanics. We introduce a general principle of mechanical stability and derive a necessary…
In this article a notion of information is presented which stresses the contextuality of quantum objects and their measurement. Mathematically this is reached by a quantification of the quantum mechanical surplus knowledge which has been…
Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of light $c$ not being infinite calls for a redefinition of space-time on large and cosmological scales,…
On the basis of a general action principle, we revisit the scale invariant field equation using the co-tensor relations by Dirac (1973). This action principle also leads to an expression for the scale factor $\lambda$, which corresponds to…
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
Quantum theory imposes fundamental limitations to the amount of information that can be carried by any quantum system. On the one hand, Holevo bound rules out the possibility to encode more information in a quantum system than in its…