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A challenging frontier in modern statistical physics concerns systems with a small number of degrees of freedom, far from the thermodynamic limit. Beyond the general interest in the foundation of statistical mechanics, the relevance of this subject is due to the recent increase of resolution in the observation and manipulation of biological and manmade objects at micro and nanoscales. A peculiar feature of small systems is the role played by fluctuations, which cannot be neglected and are responsible for many nontrivial behaviors. The study of fluctuations of thermodynamic quantities, such as energy or entropy, goes back to Einstein, Onsager, and Kubo; more recently, interest in this matter has grown with the establishment of new fluctuation–dissipation relations, and of socalled stochastic thermodynamics. This turning point has received a strong impulse from the study of systems that are far from the thermodynamic equilibrium, due to very long relaxation times, as in disordered systems, or due to the presence of external forcing and dissipation, as in granular or active matter. Applications of the thermodynamic and statistical mechanics of small systems range from molecular biology to micromechanics, including models of nanotransport, Brownian motors, and (living or artificial) selfpropelled organisms.
Statistical Mechanics  Small Systems  Stochastic Thermodynamics  NonEquilibrium Fluctuations  Large Deviations
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This Special Issue "Differential Geometrical Theory of Statistics" collates selected invited and contributed talks presented during the conference GSI'15 on "Geometric Science of Information" which was held at the Ecole Polytechnique, ParisSaclay Campus, France, in October 2015 (Conference web site: http://www.see.asso.fr/gsi2015).
Entropy  Coding Theory  Maximum entropy  Information geometry  Computational Information Geometry  Hessian Geometry  Divergence Geometry  Information topology  Cohomology  Shape Space  Statistical physics  Thermodynamics
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For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for noncommutative harmonic analysis, applied to locallycompact, nonAbelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. 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. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring noncommutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.
WeylHeisenberg group  affine group  Weyl quantization  Wigner function  covariant integral quantization  Fourier analysis  special functions  rigged Hilbert spaces  quantum mechanics  signal processing  nonFourier heat conduction  thermal expansion  heat pulse experiments  pseudotemperature  GuyerKrumhansl equation  higher order thermodynamics  Lie groups thermodynamics  homogeneous manifold  polysymplectic manifold  dynamical systems  nonequivariant cohomology  Lie group machine learning  SouriauFisher metric  Born–Jordan quantization  shorttime propagators  timeslicing  Van Vleck determinant  thermodynamics  symplectization  metrics  nonequilibrium processes  interconnection  discrete multivariate sine transforms  orthogonal polynomials  cubature formulas  nonequilibrium thermodynamics  variational formulation  nonholonomic constraints  irreversible processes  discrete thermodynamic systems  continuum thermodynamic systems  fourier transform  rigid body motions  partial differential equations  Lévy processes  Lie Groups  homogeneous spaces  stochastic differential equations  harmonic analysis on abstract space  heat equation on manifolds and Lie Groups
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Molecular magnets show many properties not met in conventional metallic magnetic materials, i.e. low density, transparency to electromagnetic radiation, sensitivity to external stimuli such as light, pressure, temperature, chemical modification or magnetic/electric fields, and others. They can serve as “functional” materials in sensors of different types or be applied in highdensity magnetic storage or nanoscale devices. Research into moleculebased materials became more intense at the end of the 20th century and is now an important branch of modern science. The articles in this Special Issue, written by physicists and chemists, reflect the current work on molecular magnets being carried out in several research centers. Theoretical papers in the issue concern the influence of spin anisotropy in the low dimensional lattice of the resulting type of magnet, as well as thermodynamics and magnetic excitations in spin trimers. The impact of external pressure on structural and magnetic properties and its underlying mechanisms is described using the example of Prussian blue analogue data. The other functionality discussed is the magnetocaloric effect, investigated in coordination polymers and high spin clusters. In this issue, new molecular magnets are presented: (i) ferromagnetic highspin [Mn6] singlemolecule magnets, (ii) solvatomagnetic compounds changing their structure and magnetism dependent on water content, and (iii) a family of purely organic magnetic materials. Finally, an advanced calorimetric study of anisotropy in magnetic molecular superconductors is reviewed.
Heisenberg  S = 1/2 XXZ model  spin anisotropy  square lattice  chain  rectangular lattice  BerezinskiiKosterlitzThouless phase transition  phase diagram  quantum magnet  molecular magnets  magnetocaloric effect  octacyanometallates  critical behaviour  coordination polymers  manganese(III)  salicylamidoxime  molecular magnetism  singlemolecule magnets  radical anion  redox  magnetism  antiferromagnetic coupling  dioxothiadiazole  molecular magnetism  octacyanotungstate(V)  copper(II)  cyclam  cyano bridge  magnetic properties  ?d system  thermodynamic measurement  superconductivity  antiferromagnetism  single crystal heat capacity measurement  magnetic conductor  molecular magnets  spin clusters  Heisenberg exchange Hamiltonian  thermodynamics  inelastic neutron scattering  exact diagonalization  Prussian blue analogues  effect of high pressure  crystal structure  magnetic properties  superexchange interaction
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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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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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There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new nonperturbative theory, such as statistical description. Furthermore, multiscale interactions are responsible for inevitably complex dynamics in strongly nonequilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multiscale interaction, a quasiequilibrium state (the socalled selforganisation) can however be maintained. This special issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. The 14 contributions to this Special issue focus on the various aspects of intermittency, coherent structures, selforganisation, bifurcation and nonlocality. Given the ubiquity of turbulence, the contributions cover a broad range of systems covering laboratory fluids (channel flow, the Von Kármán flow), plasmas (magnetic fusion), laser cavity, wind turbine, air flow around a highspeed train, solar wind and industrial application.
pipe flow boundary layer  turbulent transition  large eddy simulation  channel flow  kinetic theory  fluid dynamics  turbulence  selforganisation  shear flows  coherent structures  turbulence  stochastic processes  Langevin equation  FokkerPlanck equation  information length  trailingedge flap  control strategy  floating wind turbine  turbulence  free vortex wake  nonlocal theory  Lévy noise  Tsallis entropy  fractional Fokker–Plank equation  anomalous diffusion  hybrid (U)RANSLES  IDDES methodology  attached and separated flows  complex dynamics  microcavity laser  spatiotemporal chaos  turbulent boundary layer  low speed streaks  magnetic confinement fusion  turbulence  heat transport  Tjunction  denoise  coherent structure  continuous wavelet transform  solar wind  scaling properties  fractals  chaos  turbulence  intermittency  multifractal  thermodynamics  drop breakage  drop coalescence  local intermittency  turbulent flow  population balance equation  high efficiency impeller  Rushton turbine  energy cascade  bifurcations  Lyapunov theory  turbulence  statistical mechanics  intermittency  coherent structure  multiscale problem  selforganisation  bifurcation  nonlocality  scaling  multifractal
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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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The amide bond represents a privileged motif in chemistry. The recent years have witnessed an explosion of interest in the development of new chemical transformations of amides. These developments cover an impressive range of catalytic N–C bond activation in electrophilic, Lewis acid, radical, and nucleophilic reaction pathways, among other transformations. Equally relevant are structural and theoretical studies that provide the basis for chemoselective manipulation of amidic resonance. This monograph on amide bonds offers a broad survey of recent advances in activation of amides and addresses various approaches in the field.
fumardiamide  primaquine  succindiamide  Michael acceptor  biofilm eradication  antibacterial screening  antiviral activity  cytostatic activity  N,Ndimethylformamide  DMF  N,Ndimethylacetamide  DMAc  amination  amidation  thioamidation  formylation  carbonylation  cyanation  insertion  cyclization  amide  arynes  insertion  activation  heterocycles  organic synthesis  multicomponent coupling reaction  aryl thioamides  thiourea  CH/CN activation  CS formation  transitionmetalfree  rotational barrier energy  amide bond  nuclear magnetic resonance  kinetic  density functional theory  non planar amide  basecatalyed hydrolysis  water solvation  entropy  transamidation  amide  amine  catalyst  catalysis  acylative crosscoupling  trialkylborane  amide activation  palladium  Nheterocyclic carbene  ruthenium (Ru)  Nheterocyclic carbenes (NHCs)  homogeneous catalysis  in situ  amide bonds  synthesis  density functional theory  cis/trans isomerization  secondary amides  dipeptides  steric effects  tertbutyl  additivity principle  amino acid transporters  amide bond  gemcitabine prodrug  metabolic stability  pancreatic cancer cells  pharmacokinetics  peptide bond cleavage  amide bond resonance  twisted amides  enzymes  metal complexes  catalysts  amide C–N bond activation  nickel catalysis  amidation  DFT study  reaction thermodynamics  amide resonance  anomeric effect  HERON reaction  pyramidal amides  physical organic chemistry  reaction mechanism  amide  activation  amidicity  carbonylicity  transamidation  acyl transfer  excited state  SuzukiMiyaura  crosscoupling  aryl esters  C–O activation  Pdcatalysis  amides  carbanions  C–H acidity  nitroaci tautomerism  molecular dynamics  densityfunctional theory  alkynes  C–H bond cleavage  C–N bond cleavage  cyclopentadienyl complexes  N(1naphthyl)acetamide  rhodium  [2+2+2] annulation  amide bond  sulfonamide bond  alkynes  addition reaction  aminoacylation  aminosulfonylation  precatalysts  palladium catalysis  amide bond activation  ester bond activation  crosscoupling  amide bond  bridged lactams  twisted amides  amides  WinklerDunitz parameters  N–C activation  hypersensitivity  nitrogen heterocycles  distortion  bridged sultams  amides  CN ? bond cleavage  sodium  crown ether  amide hydrolysis  model compound  intramolecular catalysis  twisted amide  protease  intein  CH functionalization  directing groups  amides  transition metals  catalysis
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