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The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, subRiemannian manifolds, and Lie groups. In parallel, in geometric mechanics, JeanMarie Souriau interpreted the temperature vector of Planck as a spacetime vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties.
uncertainty relation  Wigner–Yanase–Dyson skew information  quantum memory  Born probability rule  quantumclassical relationship  spinors in quantum and classical physics  square integrable  energy quantization  Quantum HamiltonJacobi Formalism  quantum trajectory  generalized uncertainty principle  successive measurements  minimal observable length  Rényi entropy  Tsallis entropy  deep learning  quantum computing  neuromorphic computing  high performance computing  quantum mechanics  Gleason theorem  Kochen–Specker theorem  Born rule  quantum uncertainty  quantum foundations  quantum information  continuous variables  Bohmian dynamics  entanglement indicators  linear entropy  original Bell inequality  perfect correlation/anticorrelation  qudit states  quantum bound  measure of classicality  foundations of quantum mechanics  uncertainty relations  bell inequalities  entropy  quantum computing
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The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics—in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.
quantum logic  groups  partially defined algebras  quasigroups  viable cultures  quantum information theory  bit commitment  protocol  entropy  entanglement  orthogonality  quantum computation  Gram–Schmidt process  quantum probability  potentiality  complementarity  uncertainty relations  Copenhagen interpretation  indefiniteness  indeterminism  causation  randomness  quantum information  quantum dynamics  entanglement  algebra  causality  geometry  probability  quantum information theory  realism  reality  entropy  correlations  qubits  probability representation  Bayes’ formula  quantum entanglement  threequbit random states  entanglement classes  entanglement polytope  anisotropic invariants  quantum random number  vacuum state  maximization of quantum conditional minentropy  quantum logics  quantum probability  holistic semantics  epistemic operations  Bell inequalities  algorithmic complexity  Borel normality  Bayesian inference  model selection  random numbers  quantumlike models  operational approach  information interpretation of quantum theory  social laser  social energy  quantum information field  social atom  Bose–Einstein statistics  bandwagon effect  social thermodynamics  resonator of social laser  master equation for socioinformation excitations  quantum contextuality  Kochen–Specker sets  MMP hypergraphs  Greechie diagrams  quantum foundations  probability  irreducible randomness  random number generators  quantum technology  entanglement  quantumlike models for social stochasticity  contextuality
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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in ""deeperlevel"" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de BroglieBohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeperlevel questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and nonclassical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.
quantum foundations  nonlocality  retrocausality  Bell’s theorem  Bohmian mechanics  quantum theory  surrealistic trajectories  Bell inequality  quantum mechanics  generalized Lagrangian paths  covariant quantum gravity  emergent spacetime  Gaussianlike solutions  entropy and time evolution  resonances in quantum systems  the Friedrichs model  complex entropy.  Bell’s theorem  the causal arrow of time  retrocausality  superdeterminism  toymodels  quantum ontology  subquantum dynamics  microconstituents  emergent spacetime  emergent quantum gravity  entropic gravity  black hole thermodynamics  SternGerlach  trajectories  spin  Bell theorem  fractal geometry  padic metric  singular limit  gravity  conspiracy  free will  number theory  quantum potential  Feynman paths  weak values  Bohm theory  nohiddenvariables theorems  observables  measurement problem  Bohmian mechanics  primitive ontology  Retrocausation  weak values  Stochastic Electrodynamics  quantum mechanics  decoherence  interpretations  pilotwave theory  Bohmian mechanics  Born rule statistics  measurement problem  quantum thermodynamics  strong coupling  operator thermodynamic functions  quantum theory  de Broglie–Bohm theory  contextuality  atomsurface scattering  bohmian mechanics  matterwave optics  diffraction  vortical dynamics  Schrödinger equation  de Broglie–Bohm theory  nonequilibrium thermodynamics  zeropoint field  de Broglie–Bohm interpretation of quantum mechanics  pilot wave  interiorboundary condition  ultraviolet divergence  quantum field theory  Aharonov–Bohm effect  physical ontology  nomology  interpretation  gauge freedom  Canonical Presentation  relational space  relational interpretation of quantum mechanics  measurement problem  nonlocality  discrete calculus  iterant  commutator  diffusion constant  LeviCivita connection  curvature tensor  constraints  Kilmister equation  Bianchi identity  stochastic differential equations  Monte Carlo simulations  Burgers equation  Langevin equation  fractional velocity  interpretations of quantum mechanics  David Bohm  mind–body problem  quantum holism  fundamental irreversibility  spacetime fluctuations  spontaneous state reduction  Poincaré recurrence  symplectic camel  quantum mechanics  Hamiltonian  molecule interference  matterwaves  metrology  magnetic deflectometry  photochemistry  past of the photon  Mach–Zehnder interferometer  Dove prism  photon trajectory  weak measurement  transition probability amplitude  atomic metastable states  Bell’s theorem  Bohmian mechanics  nonlocality  many interacting worlds  wavefunction nodes  bouncing oil droplets  stochastic quantum dynamics  de Broglie–Bohm theory  quantum nonequilibrium  Htheorem  ergodicity  ontological quantum mechanics  objective nonsignaling constraint  quantum inaccessibility  epistemic agent  emergent quantum state  selfreferential dynamics  dynamical chaos  computational irreducibility  undecidable dynamics  Turing incomputability  quantum ontology  nonlocality  timesymmetry  retrocausality  quantum causality  conscious agent  emergent quantum mechanics  Bohmian mechanics  de BroglieBohm theory
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