Some Remarks on Classical and Classical-Quantum Sphere Packing Bounds: Rényi vs. Kullback–Leibler

Information is physical, so its manipulation through devices is subject to its own mechanics: the science and engineering of behavioral description, which is intermingled with classical, quantum and statistical mechanics principles. This chapter is a unification of these principles and physical laws with their implications for nanoscale. Ideas of state machines, Church-Turing thesis and its embodiment in various state machines, probabilities, Bayesian principles and entropy in its various forms (Shannon, Boltzmann, von Neumann, algorithmic) with an eye on the principle of maximum entropy as an information manipulation tool. Notions of conservation and non-conservation are applied to example circuit forms folding in adiabatic, isothermal, reversible and irreversible processes. This brings out implications of fluctuation and transitions, the interplay of errors and stability and the energy cost of determinism. It concludes discussing networks as tools to understand information flow and decision making and with an introduction to entanglement in quantum computing.

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Classical, Quantum and Biological Randomness as Relative Unpredictability

Chance, Calculation and Life ◽

10.1002/9781119823971.ch1 ◽

2021 ◽

pp. 1-35

Author(s):

Cristian S. Calude ◽

Giuseppe Longo

Keyword(s):

Classical Quantum ◽

Biological Randomness

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The Rabi problem with elliptical polarization

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0181 ◽

2020 ◽

Vol 75 (11) ◽

pp. 937-962

Author(s):

Heinz-Jürgen Schmidt

Keyword(s):

Floquet Theory ◽

Equation Of Motion ◽

Quantum Spin ◽

Heun Equation ◽

Elliptical Polarization ◽

Third Order ◽

Polynomial Coefficients ◽

Resonance Frequencies ◽

Classical Quantum ◽

Elliptically Polarized

AbstractWe consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third-order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields physically interesting quantities like the quasienergy as a function of the problem’s parameters and expressions for the Bloch–Siegert shift of resonance frequencies. Various limit cases are thoroughly investigated.

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Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity

Entropy ◽

10.3390/e23080971 ◽

2021 ◽

Vol 23 (8) ◽

pp. 971

Author(s):

Oded Shor ◽

Felix Benninger ◽

Andrei Khrennikov

Keyword(s):

Experimental Data ◽

Clustering Algorithms ◽

Realistic Model ◽

Minkowski Geometry ◽

Ultrametric Spaces ◽

Chsh Inequality ◽

Classical Quantum ◽

Basic Features ◽

Totally Disconnected ◽

Explicate Order

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH theory). We used the ontic–epistemic (implicate–explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic universe is described as a p-adic tree; it is zero-dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric spaces). Classical–quantum interrelations lose their sharpness; generally, simple dendrograms are “more quantum” than complex ones. We used the CHSH inequality as a measure of quantum-likeness. We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor a rejection of realism, but the nonergodicity of dendrogramic time series. Generally, the violation of ergodicity is one of the basic features of DH theory. The dendrogramic representation leads to the local realistic model that violates the CHSH inequality. We also considered DH theory for Minkowski geometry and monitored the dependence of CHSH violation and nonergodicity on geometry, as well as a Lorentz transformation of data.

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