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# Topic: Statistical mechanics

###### In the News (Sun 26 May 19)

 Statistical mechanics - Wikipedia, the free encyclopedia Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level. However, Entropy in thermodynamics can only be known empirically, whereas in Statistical mechanics, it is a function of the distribution of the system on its micro-states. en.wikipedia.org /wiki/Statistical_mechanics   (2460 words)

 statistical mechanics. The Columbia Encyclopedia, Sixth Edition. 2001-05 The foundations of statistical mechanics can be traced to the 19th-century work of Ludwig Boltzmann, and the theory was further developed in the early 20th cent. Maxwell-Boltzmann statistics apply to systems of classical particles, such as the atmosphere, in which considerations from the quantum theory are small enough that they may be ignored. Statistical mechanics has also yielded deep insights in the understanding of magnetism, phase transitions, and superconductivity. www.bartleby.com /65/st/statmech.html   (414 words)

 FUNDAMENTALS OF STATISTICAL MECHANICS   (Site not responding. Last check: 2007-10-22) He laid the fundamentals for the theory of solids and has been called the "father of solid-state physics." His numerous, valuable contributions include the theory of magnetism, measurement of the magnetic moment of the neutron, nuclear magnetic resonance, and the infrared problem in quantum electrodynamics. Statistical mechanics is a crucial subject which explores the understanding of the physical behaviour of many-body systems that create the world around us. I found it particularly useful in "seminar classes", where students are required to read and cope with a new topic and then present it to their fellow students. www.icpress.co.uk /books/physics/4522.html   (401 words)

 Philosophy of Statistical Mechanics Statistical mechanics was the first foundational physical theory in which probabilistic concepts and probabilistic explanation played a fundamental role. The account offered by statistical mechanics of the asymmetry in time of physical processes also plays an important role in the philosopher's attempt to understand the alleged asymmetries of causation and of time itself. Philosophers dealing with statistical explanation have generally focussed on everyday uses of probability in explanation, or the use of probabilistic explanations in such disciplines as the social sciences. plato.stanford.edu /entries/statphys-statmech   (5119 words)

 JCE 2000 (77) 161 [Feb] Statistical Thermodynamics and Kinetic Theory (by Charles E. Hecht) The preface to Statistical Thermodynamics and Kinetic Theory claims that the book is acceptable for either a graduate text or as a text for part of a rigorous undergraduate physical chemistry sequence. Nonetheless, this chapter opens the door to modern techniques in statistical mechanics and is an excellent introduction to those wanting to study these methods in more detail. Hecht balances elementary statistical mechanics pedagogy with advanced topics and references to assist those wanting a deeper treatment of the subject matter. jchemed.chem.wisc.edu /Journal/Issues/2000/feb/abs161_1.html   (747 words)

 Physics 117 - Statistical Mechanics   (Site not responding. Last check: 2007-10-22) In it we explore the mechanical basis for temperature and entropy, learn why heat flows from hot to cold, why the nozzle of the propane dispenser gets freezing cold on a hot day, why ice shatters boulders, and why there is an arrow of time. Our approach to statistical mechanics and thermodynamics includes both classical and quantum mechanical views of physical systems and begins with the basic concepts of probability and statistics. The course includes the statistics of the microcanonical, canonical, and grand canonical ensembles; the relation between classical and quantum statistical mechanics; the Planck distribution, bosons, fermions, and doped semiconductors, among others; and an introduction to kinetic theory. kossi.physics.hmc.edu /courses/p117   (315 words)

 Statistical Mechanics History: Biographies Statistical mechanics, quantitative study of systems consisting of a large number of interacting elements, such as the atoms or molecules of a solid, liquid, or gas, or the individual quanta of light making up electromagnetic radiation. The foundation of statistical physics was laid towards the end of the nineteenth century by James Clerk Maxwell, Ludwig Boltzmann, Josiah Willard Gibbs and largely completed by Albert Einstein in 1905. Anyone interested in the development of classical mechanics needs to know that it grew primarily out of the kinetic theory of gases and was developed into statistical mechanics first by Ludwig Boltzmann and then by J. Willard Gibbs. sm-scientists.net   (568 words)

 Sketching the History of Statistical Mechanics and Thermodynamics   (Site not responding. Last check: 2007-10-22) Boltzmann formulates a statistical mechanical version of the second law of thermodynamics in the paper, "On the Relation Between the Second Law of the Mechanical Theory of Heat and the Probability Calculus with Respect to the Theorems on Thermal Equilibrium". Gibbs publishes Elementary Principles in Statistical Mechanics, his treatise on the subject, deriving common thermodynamic properties from particle statistics, giving his full account of ensemble theory and their relationships (including the so-called "Gibbs paradox," though there was nothing paradoxical about it at the time). Einstein publishes a paper on the photoelectric effect, basing his analysis on an analog of the statistical mechanical approach for classical electromagnetic fields modelled as quanta of light. history.hyperjeff.net /statmech.html   (6799 words)

 Statistical Mechanics   (Site not responding. Last check: 2007-10-22) In the second half of the nineteenth century a different way to describe mechanical systems was developed based on the assumption that an isolated system of particles is equally likely to be found in any possible configuration. This assumption is called the fundamental assumption of statistical mechanics, and we will explore in this experiment some consequences of this assumption and see how well they are born out by experiment. Using the fundamental assumption of statistical mechanics, you will predict how likely the divider will be found at different distances from the center position, and compare your predictions with observations. kossi.physics.hmc.edu /Courses/p23a/Experiments/StatisticalMechanics.html   (2359 words)

 Statistical Mechanics Statistical mechanics provides a bridge between the macroscopic realm of classical thermodynamics and the microscopic realm of atoms and molecules. This review of some basic principles of statistical mechanics serves as a prelude to discussions of free energy simulations. The Boltzmann distribution law that is a fundamental principle in statistical mechanics enables us to determine how a large number of particles distribute themselves throughout a set of allowed energy levels. www.biochem.vt.edu /modeling/stat_mechanics.html   (1840 words)

 mechanics --  Encyclopædia Britannica Mechanics of different trades were to learn from each other—a denial of guild... Although a number of important discoveries in mechanics were made during the next 18 centuries, it was Galileo who opened the door to an entirely new world of physics. At the age of 19 he timed with his pulse the swings of a great chandelier in the cathedral at Pisa and found that the swing always took the same time, even though the size of the excursion became smaller... www.britannica.com /eb/article-9110307   (765 words)

 Graduate Statistical Mechanics Texts Debashish Chowdhury and Dietrich Stauffer, Principles of Equilibrium Statistical Mechanics, Wiley-VCH (2000). A textbook on equilibrium statistical mechanics for advanced undergraduate and graduate students of mathematics and physics. Walter Greiner, Ludwig Neise, and Horst Stocker, Thermodynamics and Statistical Mechanics, Springer-Verlag (1995). stp.clarku.edu /grad_texts.html   (1018 words)

 statistical mechanics statistical mechanics, quantitative study of systems consisting of a large number of interacting elements, such as the atoms or molecules of a solid, liquid, or gas, or the individual quanta of light (see Bose-Einstein statistics - Bose-Einstein statistics, class of statistics that applies to elementary particles called bosons,... Versatile mechanics cut shop staff by a third: training extends the utility of specialists who had never crossed the line between truck shop and equipment shop. www.infoplease.com /ce6/sci/A0846566.html   (511 words)

 School of Physics Spring 2002 Courses: 6107 Statistical Mechanics I Before you can do so, you will have to learn to recognize when statistical ideas will be useful, what the most promising approach is likely to be, and what methods are available to solve the problem. The lectures will develop the methods of statistical mechanics systematically, and illustrate their application with numerous examples and applications to real problems. The homework will continue this theme, with a large fraction of the problems dealing with real, rather than practice, problems, many quite important in the development of statistical mechanics or in current research, as the names attached to the problems will indicate. www.physics.gatech.edu /academics/Classes/spring2002/6107   (462 words)

 [No title]   (Site not responding. Last check: 2007-10-22) There are two approaches to thermal physics, the large scale or macroscopic approach of Classical Thermodynamics, and the atomistic or microscopic approach of Statistical Mechanics. The methods used to derive the statistical distribution laws were very novel when the first edition was published, quite different from the counting techniques used in the earlier books. In some ways it follows the conventional format, treating Classical Thermodynamics and then Statistical Mechanics, but, before any of this there is a discussion of small systems and ideas from statistics, and the treatment of thermodynamics makes use of these ideas rather than taking a purely macroscopic approach. www.crab.rutgers.edu /%7Ecowley/thermal1/textbooks.htm   (1373 words)

 Statistical Mechanics links   (Site not responding. Last check: 2007-10-22) NEWS, Expectations and Trends in Statistical Mechanics, Kolymbari Crete, August 13-18, 2005. Statistical systems out of equilibrium: random systems and complex fluids, The First Australian-Italian Workshop on Statistical Physics, 13th-15th February, 2006, Legends Hotel, located at Surfers Paradise on the Gold Coast, Queensland, Australia. SEVENTH LIBLICE Conference on the Statistical Mechanics of Liquids, Trest Manor Czech Rep, June 11 - 16, 2006. rsc.anu.edu.au /~evans/sm.html   (649 words)

 Statistical Mechanics - Calculating Equilibrium Averages According to statistical mechanics, the probability that a given state with energy E is occupied in equilibrium at constant particle number N, volume The equilibrium value of any observable O is therefore obtained by averaging over all states accessible to the system, weighting each state by this factor. Quantum mechanically, this averaging is performed simply by summing over the discrete set of microstates (Figure 1): cmm.info.nih.gov /intro_simulation/node2.html   (161 words)

 Physics Today October 2000 To the (perhaps rhetorical) question raised on page 32 of the article as to whether statistical mechanics is essential to the second law, the answer is presumably "No," since the main work of Sadi Carnot and Rudolph Clausius preceded that of Willard Gibbs. The "disorder" of statistical mechanics corresponds to the homogeneity of the sea of dissipated energy, but we don't need to know this to understand the physical reality of entropy and the second law. I am not convinced, however, that their approach to entropy is "independent of any statistical model--or even of atoms." Their definition of entropy is not an operational one. www.aip.org /pt/vol-53/iss-10/p11.html   (1630 words)

 Amazon.co.uk: Introductory Statistical Mechanics: Books   (Site not responding. Last check: 2007-10-22) In this second edition, slightly more advanced material on statistical mechanics is introduced, material which students should meet in an undergraduate course. From reviews of the first edition: '...Introductory Statistical Mechanics is clear and crisp and takes advantage of the best parts of the many approaches to the subject' Physics Today. Much of the mathematical skills needed to understand and use statistical mechanics are covered in the first couple of chapters. www.amazon.co.uk /exec/obidos/ASIN/0198505760   (899 words)

 Statistical Mechanics   (Site not responding. Last check: 2007-10-22) Thermal Equilibrium, Temperature: statistical nature of equilibrium illustrated for 2 sets of N harmonic oscillators, definition of temperature, Boltzmann distribution, partition function Z, term "canonical ensemble" [2] Entropy: general statistical definition of entropy S, law of increase of entropy, entropy of isolated system in internal equilibrium ("microcanonical ensemble"), entropy of system in thermal equilibrium with a heat bath ("canonical ensemble"), Helmholtz free energy F; equivalence of classical and statistical entropy [2.5] - apply the definitions and results of statistical mechanics to deduce physical properties of the systems studied in the lectures and other systems of similar complexity, drawing in part on your knowledge of the microstates of simple systems from core courses in quantum mechanics and solid state physics. www-users.york.ac.uk /~rwg3/statmech_syllabus.html   (422 words)

 About Temperature Gibbs (1839-1903) introduced statistical mechanics with which he demonstrated how average values of the properties of a system could be predicted from an analysis of the most probable values of these properties found from a large number of identical systems (called an ensemble). Again, in the statistical mechanical interpretation of thermodynamics, the key parameter is identified with a temperature which can be directly linked to the thermodynamic temperature, with the temperature of Maxwell's distribution, and with the perfect gas law. A second mechanism of heat transport is illustrated by a pot of water set to boil on a stove - hotter water closest to the flame will rise to mix with cooler water near the top of the pot. www.unidata.ucar.edu /staff/blynds/tmp.html   (4839 words)

 Open Directory - Science: Physics: Mathematical Physics: Statistical Mechanics ArXiv Statistical Mechanics - Recent papers and preprints in Statistical Mechanics. Center for Statistical Mechanics and Mathematical Physics - An interdisciplinary center at Virginia Tech. Statistical Mechanics in a Nutshell - Lecture notes by Jochen Rau from a course on "Transport Theory" taught at Dresden University. dmoz.org /Science/Physics/Mathematical_Physics/Statistical_Mechanics   (312 words)

 Statistical Mechanics and Thermodynamics Texts The author's aim is to provide a fresh approach to the subject, setting out the basic assumptions clearly and emphasizing the importance of the thermodynamic limit and the role of convexity. Charles E. Hecht, Statistical Thermodynamics and Kinetic Theory, Dover (1998). An analysis of the conceptual foundations of statistical mechanics as formulated by Boltzmann. stp.clarku.edu /books   (1878 words)

 Frank Stillinger -- Complete Publication List Contribution to the Statistical Geometric Basis of Radiation Scattering, H. Frisch and F. Stillinger, J. Chem. Statistical Mechanical Theory of Double-Layer Structure and Properties, F. Buff and F. Stillinger, J. Chem. "A Statistical Mechanical Model for Inverse Melting," M.R. Feeney, P.G. Debenedetti, and F.H. Stillinger, J. Chem. mse-092697c.princeton.edu /publications.htm   (4418 words)

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