Advances in Physics, ISSN 0001-8732, 05/2016, Volume 65, Issue 3, pp. 239 - 362

...), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT...

eigenstate thermalization | quantum thermodynamics | quantum quench | quantum chaos | generalized Gibbs ensemble | 03.65.-w | random matrix theory | 05.30.-d | 05.45.Mt | quantum statistical mechanics | 05.70.-a | LOCALIZATION | PHYSICS, CONDENSED MATTER | ENERGY | INTEGRABILITY | CHARACTERISTIC VECTORS | FINITE FERMI SYSTEMS | 2ND LAW | BORDERED MATRICES | DYNAMICS | FLUCTUATION THEOREM | MATRIX-ELEMENTS | Thermodynamics | Theorems | Chaos theory | Dynamics | Fluctuation | Mathematical models | Statistical mechanics | Dynamical systems

eigenstate thermalization | quantum thermodynamics | quantum quench | quantum chaos | generalized Gibbs ensemble | 03.65.-w | random matrix theory | 05.30.-d | 05.45.Mt | quantum statistical mechanics | 05.70.-a | LOCALIZATION | PHYSICS, CONDENSED MATTER | ENERGY | INTEGRABILITY | CHARACTERISTIC VECTORS | FINITE FERMI SYSTEMS | 2ND LAW | BORDERED MATRICES | DYNAMICS | FLUCTUATION THEOREM | MATRIX-ELEMENTS | Thermodynamics | Theorems | Chaos theory | Dynamics | Fluctuation | Mathematical models | Statistical mechanics | Dynamical systems

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2016, Volume 458, pp. 210 - 218

The non-extensive statistical mechanics has been used to describe a variety of complex systems...

Nonextensivity | Generalized statistical mechanics | Canonical ensemble | Tsallis entropy | TSALLIS THERMOSTATISTICS | PHYSICS, MULTIDISCIPLINARY | DISTRIBUTIONS | TRANSITION | ANOMALOUS DIFFUSION | THERMODYNAMICS | POSSIBLE DIVERGENCES | CLUSTERS | UNSTABLE SYSTEMS | NEGATIVE HEAT-CAPACITY | ENTROPY | Reservoirs

Nonextensivity | Generalized statistical mechanics | Canonical ensemble | Tsallis entropy | TSALLIS THERMOSTATISTICS | PHYSICS, MULTIDISCIPLINARY | DISTRIBUTIONS | TRANSITION | ANOMALOUS DIFFUSION | THERMODYNAMICS | POSSIBLE DIVERGENCES | CLUSTERS | UNSTABLE SYSTEMS | NEGATIVE HEAT-CAPACITY | ENTROPY | Reservoirs

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 04/2016, Volume 447, pp. 85 - 99

The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems...

Nonextensivity | Generalized statistical mechanics | Canonical ensemble | Tsallis entropy | LAW | PHYSICS, MULTIDISCIPLINARY | DISTRIBUTIONS | PRESSURE | THERMODYNAMICS | TEMPERATURE | NONEXTENSIVE THERMOSTATISTICS | SYSTEMS | VARIABLES | TSALLIS STATISTICS | ENTROPY | Reservoirs | Maximization | Mathematical analysis | Bolts | Entropy | Statistical mechanics | Statistics | Physics - Statistical Mechanics

Nonextensivity | Generalized statistical mechanics | Canonical ensemble | Tsallis entropy | LAW | PHYSICS, MULTIDISCIPLINARY | DISTRIBUTIONS | PRESSURE | THERMODYNAMICS | TEMPERATURE | NONEXTENSIVE THERMOSTATISTICS | SYSTEMS | VARIABLES | TSALLIS STATISTICS | ENTROPY | Reservoirs | Maximization | Mathematical analysis | Bolts | Entropy | Statistical mechanics | Statistics | Physics - Statistical Mechanics

Journal Article

International Journal of Modern Physics B, ISSN 0217-9792, 04/2016, Volume 30, Issue 9, p. 1630008

.... This paper was a breakthrough in exact statistical mechanics, after Yang [Phys. Rev. Lett. 19, 1312 (1967)] published his seminal work on the discovery of the Yang...

quantum criticality | Yang-Yang thermodynamic Bethe ansatz equation | Haldane generalized exclusion statistics | Lieb-Liniger model | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | MANY-BODY PROBLEM | MODEL | PHYSICS, MATHEMATICAL | BOSONS | ONE-DIMENSION | THERMODYNAMICS | FRACTIONAL-STATISTICS | MULTICOMPONENT FERMI GAS | Thermodynamics | Analysis | Methods

quantum criticality | Yang-Yang thermodynamic Bethe ansatz equation | Haldane generalized exclusion statistics | Lieb-Liniger model | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | MANY-BODY PROBLEM | MODEL | PHYSICS, MATHEMATICAL | BOSONS | ONE-DIMENSION | THERMODYNAMICS | FRACTIONAL-STATISTICS | MULTICOMPONENT FERMI GAS | Thermodynamics | Analysis | Methods

Journal Article

Entropy, ISSN 1099-4300, 2016, Volume 18, Issue 10, pp. 370 - 370

.... Souriau, in statistical mechanics and thermodynamics. The generalization of the notion of thermodynamic equilibrium in which the one-dimensional group of time...

Poisson structures | Lagrangian formalism | Generalized Gibbs states | Momentum maps | Symplectic manifolds | Symmetry groups | Hamiltonian formalism | Thermodynamic equilibria | thermodynamic equilibria | PHYSICS, MULTIDISCIPLINARY | symplectic manifolds | momentum maps | generalized Gibbs states | symmetry groups | INFORMATION-THEORY | Thermodynamics | Mathematical analysis | Lie groups | Entropy | Statistical mechanics | Translations | Formalism | Thermodynamic equilibrium

Poisson structures | Lagrangian formalism | Generalized Gibbs states | Momentum maps | Symplectic manifolds | Symmetry groups | Hamiltonian formalism | Thermodynamic equilibria | thermodynamic equilibria | PHYSICS, MULTIDISCIPLINARY | symplectic manifolds | momentum maps | generalized Gibbs states | symmetry groups | INFORMATION-THEORY | Thermodynamics | Mathematical analysis | Lie groups | Entropy | Statistical mechanics | Translations | Formalism | Thermodynamic equilibrium

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 05/2015, Volume 91, Issue 5, p. 052106

Stationary and time-dependent solutions of a nonlinear Kramers equation, as well as its associated nonlinear Fokker-Planck equations, are investigated within the context of Tsallis nonextensive statistical mechanics...

ANOMALOUS DIFFUSION | BOLTZMANN | PHYSICS, FLUIDS & PLASMAS | GENERALIZED ENTROPIES | DYNAMICS | H-THEOREM | PHYSICS, MATHEMATICAL | FOKKER-PLANCK EQUATIONS

ANOMALOUS DIFFUSION | BOLTZMANN | PHYSICS, FLUIDS & PLASMAS | GENERALIZED ENTROPIES | DYNAMICS | H-THEOREM | PHYSICS, MATHEMATICAL | FOKKER-PLANCK EQUATIONS

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 227, Issue 1, pp. 51 - 58

Computational applications of the nonextensive entropy S q and nonextensive statistical mechanics, a current generalization of the Boltzmann–Gibbs (BG...

Entropy | Nonlinear dynamical systems | Nonextensive statistical mechanics | Numerical applications | MATHEMATICS, APPLIED | MOLECULAR-DYNAMICS | GENERALIZED-ENSEMBLE APPROACH | SIMULATED ANNEALING ALGORITHMS | MONTE-CARLO | ANOMALOUS DIFFUSION | PROTEIN-FOLDING PROBLEM | RANDOM NUMBER GENERATOR | CONFORMATIONAL-ANALYSIS | CENTRAL-LIMIT-THEOREM | TSALLIS STATISTICS

Entropy | Nonlinear dynamical systems | Nonextensive statistical mechanics | Numerical applications | MATHEMATICS, APPLIED | MOLECULAR-DYNAMICS | GENERALIZED-ENSEMBLE APPROACH | SIMULATED ANNEALING ALGORITHMS | MONTE-CARLO | ANOMALOUS DIFFUSION | PROTEIN-FOLDING PROBLEM | RANDOM NUMBER GENERATOR | CONFORMATIONAL-ANALYSIS | CENTRAL-LIMIT-THEOREM | TSALLIS STATISTICS

Journal Article

EPL (Europhysics Letters), ISSN 0295-5075, 09/2006, Volume 75, Issue 6, pp. 861 - 867

To check the validity of the theory of nonextensive statistical mechanics, we have investigated the nonextensive degree of the solar interior and have tried to find the experimental evidence...

PLANCK | TSALLIS GENERALIZED ENTROPY | QUASI-EQUILIBRIUM STATES | INSTABILITY | BOLTZMANN | THERMODYNAMICS | PHYSICS, MULTIDISCIPLINARY | SELF-GRAVITATING SYSTEMS | GRAVOTHERMAL CATASTROPHE | DARK-MATTER | JEANS CRITERION

PLANCK | TSALLIS GENERALIZED ENTROPY | QUASI-EQUILIBRIUM STATES | INSTABILITY | BOLTZMANN | THERMODYNAMICS | PHYSICS, MULTIDISCIPLINARY | SELF-GRAVITATING SYSTEMS | GRAVOTHERMAL CATASTROPHE | DARK-MATTER | JEANS CRITERION

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 07/2018, Volume 2018, Issue 7, p. 73405

In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear...

Cavity and replica method | random matrix theory and extensions | statistical inference | MECHANICS | cavity and replica method | CONFIDENCE-INTERVALS | SPIN-GLASS | REGULARIZATION | PHYSICS, MATHEMATICAL | GENERALIZED LINEAR-MODELS

Cavity and replica method | random matrix theory and extensions | statistical inference | MECHANICS | cavity and replica method | CONFIDENCE-INTERVALS | SPIN-GLASS | REGULARIZATION | PHYSICS, MATHEMATICAL | GENERALIZED LINEAR-MODELS

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 04/2012, Volume 26, Issue 10, p. 1250060

.... The dynamics can be physically interpreted in terms of fluctuating virtual momenta. This model leads to a generalized statistical mechanics that distinguishes fundamental...

Vacuum fluctuations | generalized statistical mechanics | chaotic strings | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | SUPERSTATISTICS | PHYSICS, MATHEMATICAL | COUPLED TCHEBYSCHEFF MAPS

Vacuum fluctuations | generalized statistical mechanics | chaotic strings | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | SUPERSTATISTICS | PHYSICS, MATHEMATICAL | COUPLED TCHEBYSCHEFF MAPS

Journal Article

EPL (Europhysics Letters), ISSN 0295-5075, 12/2008, Volume 84, Issue 6, pp. 60006 - 60006(3)

.... In particular, the so-called q-average is widely used in the field of nonextensive statistical mechanics...

PHYSICS, MULTIDISCIPLINARY | GENERALIZED ENTROPIES | STABILITY

PHYSICS, MULTIDISCIPLINARY | GENERALIZED ENTROPIES | STABILITY

Journal Article

Contemporary Physics, ISSN 0010-7514, 07/2009, Volume 50, Issue 4, pp. 495 - 510

The formalism of statistical mechanics can be generalised by starting from more general measures of information than the Shannon entropy and maximising those subject to suitable constraints...

entropy | complex systems | generalised statistical mechanics | measures of information | Measures of information | Entropy | Generalised statistical mechanics | Complex systems | DISTRIBUTIONS | STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | MODEL | TSALLIS ENTROPY | Physics - Statistical Mechanics

entropy | complex systems | generalised statistical mechanics | measures of information | Measures of information | Entropy | Generalised statistical mechanics | Complex systems | DISTRIBUTIONS | STATISTICAL-MECHANICS | PHYSICS, MULTIDISCIPLINARY | MODEL | TSALLIS ENTROPY | Physics - Statistical Mechanics

Journal Article

Catalysis Today, ISSN 0920-5861, 07/2005, Volume 105, Issue 1, pp. 17 - 35

Knowledge of the surface composition and atomic geometry is a prerequisite for understanding the physical and chemical properties of modern materials such as...

Atomistic thermodynamics | Surface | Phase transition | ALKALI-METAL ADSORPTION | CHEMISORPTION | surface | HIGH-TEMPERATURE | SILVER | CHEMISTRY, PHYSICAL | CO OXIDATION | GENERALIZED GRADIENT APPROXIMATION | atomistic thermodynamics | ENGINEERING, CHEMICAL | MODEL SELECTION | SUBSURFACE OXYGEN | OXIDE-FILM | phase transition | CHEMISTRY, APPLIED | DIAGRAM | Heterogeneous catalysis | Thermodynamics | Algorithms | Transition metal compounds | Atmospheric nucleation | Oxides | Corrosion and anti-corrosives

Atomistic thermodynamics | Surface | Phase transition | ALKALI-METAL ADSORPTION | CHEMISORPTION | surface | HIGH-TEMPERATURE | SILVER | CHEMISTRY, PHYSICAL | CO OXIDATION | GENERALIZED GRADIENT APPROXIMATION | atomistic thermodynamics | ENGINEERING, CHEMICAL | MODEL SELECTION | SUBSURFACE OXYGEN | OXIDE-FILM | phase transition | CHEMISTRY, APPLIED | DIAGRAM | Heterogeneous catalysis | Thermodynamics | Algorithms | Transition metal compounds | Atmospheric nucleation | Oxides | Corrosion and anti-corrosives

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2019, Volume 533, p. 122031

For non-equilibrium systems in a steady state we present two necessary and sufficient conditions for the emergence of q-canonical ensembles, also known as...

Temperature | Tsallis statistics | Generalized ensembles | PHYSICS, MULTIDISCIPLINARY | Physics - Statistical Mechanics

Temperature | Tsallis statistics | Generalized ensembles | PHYSICS, MULTIDISCIPLINARY | Physics - Statistical Mechanics

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 11/2005, Volume 72, Issue 5, p. 056133

Complex nonequilibrium systems are often effectively described by a "statistics of a statistics", in short, a "superstatistics". We describe how to proceed...

TURBULENCE | BOLTZMANN | HIGH-REYNOLDS-NUMBER | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | GENERALIZED STATISTICAL-MECHANICS | Physics - Statistical Mechanics

TURBULENCE | BOLTZMANN | HIGH-REYNOLDS-NUMBER | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | GENERALIZED STATISTICAL-MECHANICS | Physics - Statistical Mechanics

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2008, Volume 54, Issue 4, pp. 1500 - 1513

Discrete-input two-dimensional (2D) Gaussian channels with memory represent an important class of systems, which appears extensively in communications and...

Heart | Guo-Shamai-VerdÚ (GSV) theorem | Cluster variation method | magnetic recording channels | maximum a posteriori (MAP) estimation | intersymbol interference (ISI) | Estimation theory | two-dimensional (2-D) channels | multiple-access (MA) channels | information rate | Physics | Information rates | Shannon-McMillan-Breiman (SMB) theorem | Graphical models | Land mobile radio cellular systems | generalized belief propagation (GBP) | Inference algorithms | Gaussian channels | Information theory | Belief propagation | Two-dimensional (2-D) channels | Guo-Shamai-Verdú (GSV) theorem | Multiple-access (MA) channels | Information rate | Maximum a posteriori (MAP) estimation | Magnetic recording channels | Generalized belief propagation (GBP) | Intersymbol interference (ISI) | EQUALIZATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | Guo-Shamai-Verdd (GSV) theorem | ENGINEERING, ELECTRICAL & ELECTRONIC | cluster variation method | CODES | propagation (GBP) | ERROR | generalized belief | Analysis | Gaussian processes | Theorems | Gaussian | Statistical mechanics | Two dimensional | Estimators | Channels | Optimization

Heart | Guo-Shamai-VerdÚ (GSV) theorem | Cluster variation method | magnetic recording channels | maximum a posteriori (MAP) estimation | intersymbol interference (ISI) | Estimation theory | two-dimensional (2-D) channels | multiple-access (MA) channels | information rate | Physics | Information rates | Shannon-McMillan-Breiman (SMB) theorem | Graphical models | Land mobile radio cellular systems | generalized belief propagation (GBP) | Inference algorithms | Gaussian channels | Information theory | Belief propagation | Two-dimensional (2-D) channels | Guo-Shamai-Verdú (GSV) theorem | Multiple-access (MA) channels | Information rate | Maximum a posteriori (MAP) estimation | Magnetic recording channels | Generalized belief propagation (GBP) | Intersymbol interference (ISI) | EQUALIZATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | Guo-Shamai-Verdd (GSV) theorem | ENGINEERING, ELECTRICAL & ELECTRONIC | cluster variation method | CODES | propagation (GBP) | ERROR | generalized belief | Analysis | Gaussian processes | Theorems | Gaussian | Statistical mechanics | Two dimensional | Estimators | Channels | Optimization

Journal Article