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4. Canonical ensemble

4. Canonical ensembleIn this chapter we will formulate statistical physics for subsystemsthat are held at constant temperature. In the next chapter we willwork at constant temperature and constant chemical potential. Thecalculations are different from those we have done so far, and oftenfar simpler. For systems at fixed temperature there are very usefulnumerical techniques, Monte Carlo methods, that we will :Gibbs gave odd names to methods involving subsystemsin contact with reservoirs. In closed system, with fixed energy we estimate time averages bysampling uniformly over the energy shell, as we have done untilnow.

is thought to vibrate independently. In fact, all of them are coupled so that the real excitations are waves of vibration, e.g. sound waves. The Hamiltonian is quadratic in the amplitude and momentum of the waves, and we have as many different waves as we have degrees of freedom. How this works out – the normal mode transformation – will

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