By L D Landau
A lucid presentation of statistical physics and thermodynamics which develops from the overall ideas to provide plenty of functions of the idea.
Read or Download Statistical Physics, Part 1 (Course of Theoretical Physics, Vol. 5) PDF
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Additional resources for Statistical Physics, Part 1 (Course of Theoretical Physics, Vol. 5)
Is dwq = I 1p 12 dq. For a mixed state, the products c:cm are replaced by the elements Wmn of the statistical matrix, and I V'l 2 thus becomes By the definition of the matrix elements, Lm Wmn"Pm = W1pn, and so Thus we have the following formula for the coordinate probability distribution: dwq = L 1p:W1pn ·dq. 8) n In this expression the functions 'Pn may be any complete set of normalised wave functions. 20 Fundamental Principles of Statistical Physics Let us next determine the momentum probability distribution.
It is clear that the presence of the thermostat has no effect on the statistical properties of individual small parts (subsystems) of the system considered, which in any case are not closed and are in equilibrium with the remaining parts of the system. 13). So far we have assumed that the closed system is in complete statistical equilibrium. We must now generalise the above definitions to systems in arbitrary macroscopic states (partial equilibria). Let us suppose that the system is in some state of partial equilibrium, and consider it over time intervals L1 t which are small compared with the relaxation time for complete equilibrium.
14 Fundamental Principles of Statistical Physics The existence of partial equilibria leads to the concept of macroscopic states of a system. Whereas a mechanical microscopic description of the system specifies the coordinates and momenta of every particle in the system, a macroscopic description is one which specifies the mean values ·of the physical quantities determining a particular partial equilibrium, for instance the mean: values of quantities describing separate sufficiently small but macroscopic parts of the system, each of which may be regarded 'as being in a separate equilibrium.