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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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Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultrasensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on noncausal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.
reconstruction of quantum theory  entanglement  monogamy  quantum nonlocality  conserved informational charges  limited information  complementarity  characterization of unitary group and state spaces  algebraic quantum theory  C*algebra  gelfand duality  classical context  bohrification  process theory  classical limit  purity  higherorder interference  generalised probabilistic theories  Euclidean Jordan algebras  Pauli exclusion principle  quantum foundations  Xray spectroscopy  underground experiment  silicon drift detector  measurement uncertainty relations  relative entropy  position  momentum  quantum mechanics  the measurement problem  collapse models  Xrays  quantum gravity  discrete spacetime  causal sets  path summation  entropic gravity  physical computing models  complexity classes  causality  blind source separation (BSS)  qubit pair  exchange coupling  entangled pure state  unentanglement criterion  probabilities in quantum measurements  independence of random quantum sources  iterant  Clifford algebra  matrix algebra  braid group  Fermion  Dirac equation  quantum information  quantum computation  semiclassical physics  quantum control  quantum genetic algorithm  samplingbased learning control (SLC)  quantum foundations  relativity  quantum gravity  cluster states  multipartite entanglement  percolation  Shannon information  quantum information  quantum measurements  consistent histories  incompatible frameworks  single framework rule  probability theory  entropy  quantum relative entropy  quantum information  quantum mechanics  inference  quantum measurement  quantum estimation  macroscopic quantum measurement  quantum annealing  adiabatic quantum computing  hard problems  Hadamard matrix  binary optimization  reconstruction of quantum mechanics  conjugate systems  Jordan algebras  quantum correlations  Gaussian states  Gaussian unitary operations  continuousvariable systems  Wignerfriend experiment  nogo theorem  quantum foundations  interpretations of quantum mechanics  subsystem  agent  conservation of information  purification  group representations  commuting subalgebras  quantum walks  Hubbard model  Thirring model  quantum information  quantum foundations  quantum theory and gravity
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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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Modern information communication technology eradicates barriers of geographic distances, making the world globally interdependent, but this spatial globalization has not eliminated cultural fragmentation. The Two Cultures of C.P. Snow (that of science–technology and that of humanities) are drifting apart even faster than before, and they themselves crumble into increasingly specialized domains. Disintegrated knowledge has become subservient to the competition in technological and economic race leading in the direction chosen not by the reason, intellect, and shared valuebased judgement, but rather by the whims of autocratic leaders or fashion controlled by marketers for the purposes of political or economic dominance. If we want to restore the authority of our best available knowledge and democratic values in guiding humanity, first we have to reintegrate scattered domains of human knowledge and values and offer an evolving and diverse vision of common reality unified by sound methodology. This collection of articles responds to the call from the journal Philosophies to build a new, networked world of knowledge with domain specialists from different disciplines interacting and connecting with other knowledgeandvaluesproducing and knowledgeandvaluesconsuming communities in an inclusive, extended, contemporary natural–philosophic manner. In this process of synthesis, scientific and philosophical investigations enrich each other—with sciences informing philosophies about the best current knowledge of the world, both natural and humanmade—while philosophies scrutinize the ontological, epistemological, and methodological foundations of sciences, providing scientists with questions and conceptual analyses. This is all directed at extending and deepening our existing comprehension of the world, including ourselves, both as humans and as societies, and humankind.
n/a  compositional hierarchy  development  dissipative structures  final cause  internalism  Second Law of thermodynamics  subsumptive hierarchy  agonism  apophasis  autocatalysis  centripetality  contingency  endogenous selection  heterogeneity  indeterminacy  process  mathematics  physics  philosophical foundations  natural philosophy  the logic of nature  ontology  epistemology  in the name of nature  philosophy of information  natural philosophy  metaphysics  physics  problem of induction  physicalism  theoretical unity  philosophy of science  scientific method  scientific progress  pessimistic induction  awareness  cognition  computation  cybernetics  differentiation  fitness  holographic encoding  memory  perception  quantum information  signal transduction  spatial representation  thermodynamics  unitarity  Leibniz  monad  internal quantum state  relational biology  reflexive psychology  self  induction  naturalism  evidence and justification  epistemic norms  induction and concept formation  induction and discovery of laws  natural philosophy  R.M. Unger  L. Smolin  Aristotle  F.W.J. Schelling  Naturphilosophie  A.N. Whitehead  Ivor Leclerc  dialectics  discourse  discursive space  information  knowledge  humanistic management  language  natural philosophy  subjective experience  process  dual aspects  consciousness  informationtheory  theoretical biology  1stperson and 3rdperson perspectives  hylomorphism  mind  form  matter  neurodynamics  natural philosophy  philosophy of science  Jungian psychology  depth psychology  analytical psychology  phenomenological psychology  evolutionary psychology  active imagination  Aristotle’s four causes  aesthetics in science  philosophy as a way of life  common good  contradiction  ethics  information  logic  naturalization  realism  science  synthesis  natural philosophy  philosophy of nature  naturalism  unity of knowledge  qualitative ontology  intentionality  dispositions  qualia  abduction  agentbased reasoning  creativity  ecocognitive model  ecocognitive openness  fallacies  errors of reasoning  thirdway reasoning  naturalization of logic  causality  embodiment  measurement  regulation  retrocausality  secondperson description  symmetry breaking  temporality  natural philosophy  cosmology  emptiness  vacuum  void  dark energy  space flight  exoplanet  big freeze  big crunch  everyday lifeworld  digitization  computability  complexity  reverse mathematics  quantum computing  real computing  theory of everything  acategoriality  statespace approach  mental representation  dualaspect monism  exceptional experiences  intentionality  mindmatter relations  category theory  memory evolutive system  emergence  emergentist reductionism  anticipation  creativity  infocomputational model
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