From Microphysics to Macrophysics: Methods and Applications by Roger Balian (auth.)

By Roger Balian (auth.)

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O"N) that describes the system is thus the sum 0"1 + 0"2 + ... + O"N. The state of the system after a macroscopic experiment, where only a few observables are actually measured, is imperfectly known, as there are many micro-states, all corresponding to the same values of the measured observables. As is usual when insufficient information is available, one resorts to a statistical treatment. A given macroscopic state is therefore, in terms of the microscopic structure of the system, represented by a probability distribution, which we call a macro-state.

For instance, in a fluid of N particles which are randomly distributed in a large volume fl, the number n of molecules in a volume v is a random variable. 2b). 6 x 1O~8; we can thus regard nlv as being exactly determined, and equal to the density Nlfl, its statistical fluctuations being negligible compared with the experimental errors. This kind of argument will enable us to reconcile the statistical nature of microscopic physics with macroscopic determinism. Contents of the Book The first chapter is devoted to a straightforward, detailed treatment of a simple statistical physics problem ~ paramagnetism of a particular class of ionic solids.

3 from a completely general argument. InW S --N Nk In 2 p -1 1 Fig. 2. 2, confirms its interpretation as a measure of the disorder or of our uncertainty. When U is close to the ground state energy, nearly all the magnetic moments are aligned in the same direction as B; W is rather small and the system is nearly perfectly ordered. When U increases, W grows very fast - exponentially with N: the number of possible micro-states becomes larger and larger while (M) decreases and the number of magnetic moments antiparallel to the field increases.

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