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1,319 results on '"Statistical ensemble"'

1. Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement.

Author

Crisanti, Andrea, Salasnich, Luca, Sarracino, Alessandro, and Zannetti, Marco

Subjects
*CANONICAL ensemble, *SPECIFIC heat, *CONDENSED matter, *GASES, *STATISTICAL ensembles, *BOSE-Einstein condensation, *ELECTRON traps
Abstract

We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose–Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled optical microcavity under genuine grand canonical conditions, we apply our formalism to a system of non-interacting Bose particles confined in a two-dimensional harmonic trap. We discuss in detail the mathematical origin of the inequivalence of ensembles observed in the condensed phase, giving place to the so-called grand canonical catastrophe of density fluctuations. We also provide explicit analytical expressions for the internal energy and specific heat and compare them with available experimental data. For these quantities, we show the equivalence of ensembles in the thermodynamic limit. [ABSTRACT FROM AUTHOR]

Published
2024
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2. Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement

Author

Andrea Crisanti, Luca Salasnich, Alessandro Sarracino, and Marco Zannetti

Subjects
statistical ensemble, Bose–Einstein condensation, photons, Science, Astrophysics, QB460-466, Physics, QC1-999
Abstract

We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the late 1970s. Then, motivated by the Bose–Einstein condensation (BEC) of trapped gases with a fixed number of atoms, which is well described by the canonical ensemble and by the recent groundbreaking experimental realization of BEC with photons in a dye-filled optical microcavity under genuine grand canonical conditions, we apply our formalism to a system of non-interacting Bose particles confined in a two-dimensional harmonic trap. We discuss in detail the mathematical origin of the inequivalence of ensembles observed in the condensed phase, giving place to the so-called grand canonical catastrophe of density fluctuations. We also provide explicit analytical expressions for the internal energy and specific heat and compare them with available experimental data. For these quantities, we show the equivalence of ensembles in the thermodynamic limit.

Published
2024
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3. On the Foundational Principles of Statistical Mechanics

Author

Zheng, Wei-Mou, Andelman, David, Series Editor, Hu, Wenbing, Series Editor, Komura, Shigeyuki, Series Editor, Netz, Roland, Series Editor, Piazza, Roberto, Series Editor, Schall, Peter, Series Editor, Wong, Gerard, Series Editor, and Liu, Xiang-Yang, editor

Published
2021
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4. Frequentist statistical inference without repeated sampling.

Author

Vos, Paul and Holbert, Don

Abstract

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation of equally likely chance outcomes is applied to statistical inference using urn models. These are used to address Bayesian criticisms of frequentist methods. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of classical probability based on a single random sample from the population. [ABSTRACT FROM AUTHOR]

Published
2022
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5. Almost sure global well-posedness for the energy supercritical Schrödinger equations.

Author

Sy, Mouhamadou

Subjects
*INVARIANT measures, *MEASURE theory, *SOBOLEV spaces, *PROBABILITY measures, *SCHRODINGER equation, *STATISTICAL ensembles, *GIBBS sampling
Abstract

We consider the Schrödinger equations with arbitrary (large) power non-linearity on the three-dimensional torus. We construct non-trivial probability measures supported on Sobolev spaces and show that the equations are globally well-posed on the supports of these measures, respectively. Moreover, these measures are invariant under the flows that are constructed. Therefore, the constructed solutions are recurrent in time. Also, we show slow growth control on the time evolution of the solutions. A generalization to any dimension is given. Our proof relies on a new approach combining the fluctuation-dissipation method and some features of the Gibbs measures theory for Hamiltonian PDEs. The strategy of the paper applies to other contexts. [ABSTRACT FROM AUTHOR]

Published
2021
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6. The Theory of Measurement

Author

Balian, Roger, Elitzur, Avshalom C., Series editor, Merali, Zeeya, Series editor, Padmanabhan, T., Series editor, Schlosshauer, Maximilian, Series editor, Silverman, Mark P., Series editor, Tuszynski, Jack A, Series editor, Vaas, Rüdiger, Series editor, d'Espagnat, Bernard, editor, and Zwirn, Hervé, editor

Published
2017
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7. From Relational Data to Graphs: Inferring Significant Links Using Generalized Hypergeometric Ensembles

Author

Casiraghi, Giona, Nanumyan, Vahan, Scholtes, Ingo, Schweitzer, Frank, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Ciampaglia, Giovanni Luca, editor, Mashhadi, Afra, editor, and Yasseri, Taha, editor

Published
2017
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8. Elements of Quantum Statistical Mechanics

Author

Fischetti, Massimo V., Vandenberghe, William G., Becker, Kurt H., Series editor, Di Meglio, Jean-Marc, Series editor, Hassani, Sadri, Series editor, Munro, Bill, Series editor, Needs, Richard, Series editor, Rhodes, William T., Series editor, Scott, Susan, Series editor, Stanley, H. Eugene, Series editor, Stutzmann, Martin, Series editor, Wipf, Andreas, Series editor, Fischetti, Massimo V., and Vandenberghe, William G.

Published
2016
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9. One-Dimensional Systems: Exact Solution for Nearest-Neighbor Interactions

Author

Santos, Andrés, Bartelmann, Matthias, Series editor, Englert, Berthold-Georg, Series editor, Hänggi, Peter, Series editor, Hjorth-Jensen, Morten, Series editor, Jones, Richard A L, Series editor, Lewenstein, Maciej, Series editor, von Löhneysen, H., Series editor, Raimond, Jean-Michel, Series editor, Rubio, Angel, Series editor, Theisen, Stefan, Series editor, Vollhardt, Prof. Dieter, Series editor, Wells, James, Series editor, Zank, Gary P., Series editor, Salmhofer, Manfred, Series editor, and Santos, Andrés

Published
2016
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10. Spatial Correlation Functions and Thermodynamic Routes

Author

Santos, Andrés, Bartelmann, Matthias, Series editor, Englert, Berthold-Georg, Series editor, Hänggi, Peter, Series editor, Hjorth-Jensen, Morten, Series editor, Jones, Richard A L, Series editor, Lewenstein, Maciej, Series editor, von Löhneysen, H., Series editor, Raimond, Jean-Michel, Series editor, Rubio, Angel, Series editor, Theisen, Stefan, Series editor, Vollhardt, Prof. Dieter, Series editor, Wells, James, Series editor, Zank, Gary P., Series editor, Salmhofer, Manfred, Series editor, and Santos, Andrés

Published
2016
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11. Introduction

Author

Bolotin, Yurii, Tur, Anatoli, Yanovsky, Vladimir, Abarbanel, Henry, Series editor, Braha, Dan, Series editor, Érdi, Péter, Series editor, Friston, Karl, Series editor, Haken, Hermann, Series editor, Jirsa, Viktor, Series editor, Kacprzyk, Janusz, Series editor, Kaneko, Kunihiko, Series editor, Kelso, Scott, Series editor, Kirkilionis, Markus, Series editor, Kurths, Jürgen, Series editor, Nowak, Andrzej, Series editor, Menezes, Ronaldo, Series editor, Qudrat-Ullah, Hassan, Series editor, Schuster, Peter, Series editor, Schweitzer, Frank, Series editor, Sornette, Didier, Series editor, Thurner, Stefan, Series editor, Bolotin, Yurii, Tur, Anatoli, and Yanovsky, Vladimir

Published
2017
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15. Equivalence of Ensembles, Condensation and Glassy Dynamics in the Bose–Hubbard Hamiltonian.

Author

Huveneers, François and Theil, Elias

Subjects
*CONDENSATION, *STATISTICAL mechanics, *MATHEMATICAL equivalence, *STATISTICAL physics, *BOSE-Einstein condensation, *PARTICLE density (Nuclear chemistry)
Abstract

We study mathematically the equilibrium properties of the Bose–Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the microcanonical and the grand-canonical ensembles for all allowed values of the density of particles ρ and density of energy ε . Moreover, given ρ , we show that the system undergoes a transition as ε increases, from a usual positive temperature state to the infinite temperature state where a macroscopic excess of energy condensates on a single site. Analogous results have been obtained by Chatterjee [6] for a closely related model. We introduce here a different method to tackle this problem, hoping that it reflects more directly the basic understanding stemming from statistical mechanics. We discuss also how, and in which sense, the condensation of energy leads to a glassy dynamics. [ABSTRACT FROM AUTHOR]

Published
2019
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21. Transient Perturbations on Scale-Free Boolean Networks with Topology Driven Dynamics

Author

Darabos, Christian, Giacobini, Mario, Tomassini, Marco, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Kampis, George, editor, Karsai, István, editor, and Szathmáry, Eörs, editor

Published
2011
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24. Quantum gravitational effects on statistical mechanics

Author

Bosso, Pasquale, Lopez Vega, Juan Manuel, University of Lethbridge. Faculty of Arts and Science, Bosso, Pasquale, Lopez Vega, Juan Manuel, and University of Lethbridge. Faculty of Arts and Science

Abstract

Nowadays, the development of a consistent theory of quantum gravity (QG) continues to be one of the biggest challenges in physics, which has resulted in a number of potential candidates that have not been tested yet. However, phenomenology has joined this task in search of manifestations of the quantum effects of space-time. In particular, the generalized uncertainty principle (GUP) modifies the uncertainty relation between momentum and position, making room for a minimal length, as predicted by candidate theories of QG. Inspired by the GUP, we derive Planck's distribution by considering a new quantization of the electromagnetic field. We elaborate on the thermodynamics of the blackbody resulting from Wien's law and the Stefan-Boltzmann law. We demonstrate that such thermodynamic laws are modified by the presence of a minimal length. Furthermore, we consider a momentum scale in classical statistical mechanics to see its potential effects in the construction of the microcanonical ensemble.

Published
2022

27. Statistical Description of Matter

Author

Dragoman, Daniela, editor, Dragoman, Mircea, editor, Elitzur, Avshalom C., editor, Silverman, Mark P., editor, Tuszynski, Jack, editor, Zeh, H. Dieter, editor, and Kurzynski, Michal

Published
2006
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28. Simulation of Micro-, Grand-, and Canonical Ensembles of Complex Networks

Author

Biely, Christoly, Thurner, Stefan, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Alexandrov, Vassil N., editor, van Albada, Geert Dick, editor, Sloot, Peter M. A., editor, and Dongarra, Jack, editor

Published
2006
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32. The Proof and Illustration of the Central Limit Theorem by Brownian Numerical Experiments in Real Time within the Java Applet

Author

Gall, Monika, Kutner, Ryszard, Wesela, Wojciech, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Bubak, Marian, editor, van Albada, Geert Dick, editor, Sloot, Peter M. A., editor, and Dongarra, Jack, editor

Published
2004
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33. Advanced High Performance Algorithms for Data Processing

Author

Bogdanov, Alexander V., Boukhanovsky, Alexander V., Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Bubak, Marian, editor, van Albada, Geert Dick, editor, Sloot, Peter M. A., editor, and Dongarra, Jack, editor

Published
2004
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37. Nonequilibrium ensemble derivation of hydrodynamic heat transport and higher-order generalizations

Author

J. G. Ramos, Carlos A. B. Silva, Clóves G. Rodrigues, and Roberto Luzzi

Subjects
010302 applied physics, Physics, Statistical ensemble, Mesoscopic physics, General Physics and Astronomy, Motion (geometry), Non-equilibrium thermodynamics, Classical fluids, 01 natural sciences, 0103 physical sciences, Thermal, Kinetic theory of gases, Statistical physics, Contraction (operator theory)
Abstract

Thermal transport in classical fluids is analyzed through higher-order generalized hydrodynamics (or mesoscopic hydrothermodynamics) depending on the evolution of the energy density and its fluxes of all orders. It is derived by a kinetic theory based on the nonequilibrium statistical ensemble formalism. A general system of coupled evolution equations is derived. Maxwell times, which are of significance to determine the character of the motion, are derived. They also have an important role in the choice of the contraction of description (limitation in the number of fluxes to be retained) in the studies on hydrodynamic motions. In a description of order 1, an analysis of the technological process of thermal prototyping is presented.

Published
2021
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40. Statistical Description of a Physical System

Author

Salinas, Silvio R. A., Berry, R. Stephen, editor, Birman, Joseph L., editor, Lynn, Jeffrey W., editor, Silverman, Mark P., editor, Stanley, H. Eugene, editor, Voloshin, Mikhail, editor, and Salinas, Silvio R. A.

Published
2001
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41. Ensembles in statistical mechanics

Author

Kalikmanov, V. I., Balian, R., editor, Beiglböck, W., editor, Grosse, H., editor, Lieb, E. H., editor, Reshetikhin, N., editor, Spohn, H., editor, Thirring, W., editor, and Kalikmanov, V. I.

Published
2001
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42. Competition for fluctuating resources reproduces statistics of species abundance over time across wide-ranging microbiotas

Author

Kerwyn Casey Huang, Ho P, and Benjamin H. Good

Subjects
Statistical ensemble, General Immunology and Microbiology, Small number, media_common.quotation_subject, Microbiota, General Neuroscience, General Medicine, Biology, Models, Biological, Competition (biology), General Biochemistry, Genetics and Molecular Biology, Mice, Human gut, Community dynamics, Statistics, Animals, Relative species abundance, media_common
Abstract

Across diverse microbiotas, species abundances vary in time with distinctive statistical behaviors that appear to generalize across hosts, but the origins and implications of these patterns remain unclear. Here, we show that many of these macroecological patterns can be quantitatively recapitulated by a simple class of consumer-resource models, in which the metabolic capabilities of different species are randomly drawn from a common statistical distribution. Our model parametrizes the consumer-resource properties of a community using only a small number of global parameters, including the total number of resources, typical resource fluctuations over time, and the average overlap in resource-consumption profiles across species. We show that variation in these macroscopic parameters strongly affects the time series statistics generated by the model, and we identify specific sets of global parameters that can recapitulate macroecological patterns across wide-ranging microbiotas, including the human gut, saliva, and vagina, as well as mouse gut and rice, without needing to specify microscopic details of resource consumption. These findings suggest that resource competition may be a dominant driver of community dynamics. Our work unifies numerous time series patterns under a simple model, and provides an accessible framework to infer macroscopic parameters of effective resource competition from longitudinal studies of microbial communities.

Published
2022
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44. Introduction

Author

Bolotin, Yurii, Tur, Anatoli, Yanovsky, Vladimir, Bolotin, Yurii, Tur, Anatoli, and Yanovsky, Vladimir

Published
2009
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45. Statistical Ensembles

Author

Gallavotti, Giovanni, Balian, Roger, editor, Beiglböck, Wolf, editor, Grosse, Harald, editor, Lieb, Elliott H., editor, Reshetikhin, Nicolai, editor, Spohn, Herbert, editor, Thirring, Walter, editor, and Gallavotti, Giovanni

Published
1999
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46. Classical Statistical Mechanics

Author

Gallavotti, Giovanni, Balian, Roger, editor, Beiglböck, Wolf, editor, Grosse, Harald, editor, Lieb, Elliott H., editor, Reshetikhin, Nicolai, editor, Spohn, Herbert, editor, Thirring, Walter, editor, and Gallavotti, Giovanni

Published
1999
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47. First Principles of the Classical Mechanics and the Foundations of Statistical Mechanics on the Example of a Disordered Spin System

Author

V. V. Sahakyan and A. S. Gevorkyan

Subjects
Physics, Statistical ensemble, Hamiltonian mechanics, Partition function (statistical mechanics), Spin glass, 010308 nuclear & particles physics, General Physics and Astronomy, Statistical mechanics, 01 natural sciences, Equiprobability, Lattice (module), symbols.namesake, Classical mechanics, 0103 physical sciences, symbols, 010306 general physics, Spin-½
Abstract

We study the classical multicomponent disordered 3D spin system taking into account the temperature of the medium in the framework of the model of nearest neighbors. The latter allows the 3D problem with a cubic lattice to reduce to the 1D Heisenberg spin glass problem with a random environment. Using the Hamilton equations of motion, a recurrent equation is obtained that connects three spins in successive nodes of 1D lattice, taking into account the influence of a random environment. This equation, together with the corresponding conditions of a local minimum energy in nodes, allows to construct node-by-node a stable spin chains and, accordingly, to calculate all parameters of statistical ensemble from the first principles of classical mechanics, without using any additional assumptions, in particular, the main axiom of statistical mechanics – the equiprobability of statistical states. Using the example of 1D Heisenberg spin glass model, the features of the new approach are studied in detail and the statistical mechanics of the system are constructed without using the standard representation of the partition function (PF).

Published
2020
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48. Comparison of statistical ensemble methods for probabilistic nowcasting of precipitation

Author

Yang Li, Xuexing Qiu, Zhiming Kang, Yong Wang, Wei Tao, and Aitor Atencia

Subjects
Statistical ensemble, Atmospheric Science, Meteorology, Nowcasting, time-lagged method, Probabilistic logic, Environmental science, lcsh:Meteorology. Climatology, Precipitation, probabilistic precipitation forecast, lcsh:QC851-999, neighborhood method
Abstract

In the nowcasting of precipitation, predictability often varies with lead times and rain patterns. Ensemble techniques have been developed to deal with forecast uncertainty. Both “time-shifting” and “time-lagged” methods are pragmatic ensemble approaches to derive probabilistic precipitation from deterministic forecasts. This study synthesizes these two statistical probabilistic methods with customized parameters to serve different lead times and precipitation intensities. Thereafter, an integrated method is proposed by combining the time-shifting and the time-lagged methods. The performance of the three methods under various precipitation intensities and lead times is evaluated with the Brier score and Receiver Operating Characteristic curve (ROC) area. The time-shifting method is found to be superior in the forecasting of light rain. For medium precipitation, the time-shifting method gives a better Brier score while the time-lagged and integrated methods yields a higher ROC area. The advantages of the integrated method are pronounced when heavy precipitation occurs. Based on the performance of the above three methods, this study introduces a weighted index to optimize the integrated method, which gives a higher weight to time-shifting related forecasts for light and medium precipitation and keeps an equal weight for heavy rainfall. The weighting allows the integrated method to maintain or exceed the skill of the time-shifting and time-lagged methods. Afterwards, calibration is conducted based on the reliability diagram. The calibrated results outperform the raw products. Finally, a test with independent samples supports the suggestion that the presented probabilistic approach, including combination, weighting, and calibration, could be applied with confidence in an operational system.

Published
2020

49. Local Molecular Field Theory for Nonequilibrium Systems

Author

John D. Weeks, Jocelyn M. Rodgers, and Edward B. Baker

Subjects
Physics, Statistical ensemble, 010304 chemical physics, Non-equilibrium thermodynamics, 010402 general chemistry, Electrostatics, 01 natural sciences, 0104 chemical sciences, Surfaces, Coatings and Films, Formalism (philosophy of mathematics), Electric field, 0103 physical sciences, Materials Chemistry, Statistical physics, Physical and Theoretical Chemistry, Autocatalytic reaction, Confined water
Abstract

We provide a framework for extending equilibrium local molecular field (LMF) theory to a statistical ensemble evolving under a time-dependent applied field. In this context, the self-consistency of the original LMF equation is achieved dynamically, which provides an efficient method for computing the equilibrium LMF potential, in addition to providing the nonequilibrium generalization. As a concrete example, we investigate water confined between hydrophobic or charged walls, systems that are very sensitive to the treatment of long-ranged electrostatics. We then analyze confined water in the presence of a time-dependent applied electric field, generated by a sinusoidal or abrupt variation of the magnitudes of uniform charge densities on each wall. Very accurate results are found from the time-dependent LMF formalism even for strong static fields and for time-dependent systems that are driven far from equilibrium where linear response methods fail.

Published
2020
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50. Switching current of the domain ensemble with serrated charged walls

Author

E. L. Rumyantsev

Subjects
010302 applied physics, Statistical ensemble, Materials science, 02 engineering and technology, 021001 nanoscience & nanotechnology, Condensed Matter Physics, 01 natural sciences, Ferroelectricity, Electronic, Optical and Magnetic Materials, Domain (software engineering), Condensed Matter::Materials Science, 0103 physical sciences, Statistical physics, Current (fluid), 0210 nano-technology
Abstract

The time dependence of the switching current induced by the evolution of the statistical ensemble of cone-like domains in uniaxial ferroelectric is analyzed within modified Kolmogorov-Mehl-Johnson-...

Published
2020
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