"In the consistent-histories approach, the classical limit can be studies by using appropriate subspaces of the quantum as a "coarse graining," analogous to dividing up into nonoverlapping cells in classical statistical mechanics. This coarse graining can then be used to construct quantum histories. It is necessary to show that the resulting family of histories is consistent, so that the probabilities assigned by make good quantum mechanical sense. Finally, one needs to show that the resulting quantum dynamics is well approximated by appropriate classical equations."
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in a wide variety of fields such as biology, neuroscience, computer science, information theory and sociology. Its main purpose is
"I thought of calling it information, but... Von Neumann told me, You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage."
"The rapid development of quantum mechanics stimulated research in and theory. Initiated during the mid-twenties, intensive study of s and their representations led to Haars discovery of the basic construction of invariant integration on a topological group. Bohrs theory of s influenced the work of Wiener, Bochner and many other analysts. They enriched the technical arsenal of harmonic analysis and the scope of its applications (statistical mechanics, ergodic theory, , etc.) The new notion of the generalized made it possible to consider Plancherels theory simultaneously with Bohrs theory, the continuous spectrum with the discrete. The Pontrjagin-van Kampen duality opened the way for an unobstructed development of on locally compact s, allowing , Fourier integrals and expansions via numerical characters to be viewed as objects of the same kind. The Peter–Weyl theory made it possible for von Neumann to analyze almost periodic functions on groups by connecting them to group representation theory. Along with the many other discoveries of that period, this led to the inclusion of group theorethical methods into the tool kit of harmonic analysis."
"As Oliver Cromwell said to the General Assembly of the Church of Scotland, "I beseech you, in the bowels of Christ, think it possible that you might be mistaken." Life and the affairs of the living are so tangled, the world not only stranger than we imagine but stranger than we can imagine, that all questions are conundrums, no answers "correct." Is it certain that parallel lines never meet? No. Does water freeze at 32 degrees Fahrenheit? Only probably. Shall I marry? Who can say? And yet the worlds work must be done. One Oblomov is enough. Thus we learn a conventional certitude, acting as though all were light by blinking the shadow. A simple proof demonstrates that parallel lines do meet, but, on the assumption that they do not, the architect builds the skyscraper. Despite his knowledge of statistical mechanics, the engineer designs the refrigerator to maintain a constant temperature of 31 degrees. Le cœur a ses raisons que la raison ne connait pas [the heart has its reasons that reason does not know], and families are raised."
"Maxwell, and then Boltzmann, and then... J. Willard Gibbs consequently expended enormous intellectual effort in devising... statistical mechanics, or... . The uses... extend far beyond gases... describing electric and magnetic interactions, chemical reactions, phase transitions... and all other manner of exchanges of matter and energy. The success... has driven the belief among many physicists that it could be applied with similar success to society. ...[E]verything from the flow of funds in the stock market to the flow of traffic on interstate highways ..."
"As the natural sciences have developed to encompass increasingly s, scientific rationality has become ever more statistical, or probabilistic. The deterministic classical mechanics of the enlightenment was revolutionized by the near-equilibrium statistical mechanics of late 19th century atomists, by quantum mechanics in the early 20th century, and by the far-from-equilibrium complexity theorists of the later 20th century. Mathematical , information theory, and quantitative social sciences compounded the trend. Forces, objects, and natural types were progressively dissolved into statistical distributions: heterogeneous clouds, entropy deviations, s, gene frequencies, noise-signal ratios and redundancies, dissipative structures, and complex systems at the edge of chaos."
"The only important variables of interest must involve averaging over many of the degrees of freedom. Statistical mechanics is the formalization of this intuitive concept. The problems to be addressed... are threefold: under what circumstances can the properties of a physical system be defined by the behavior of an appropriate small set of variables, what are the appropriate sets of relevant variables, and how can one calculate the properties of the system in terms of these variables."