Transcription of 4. Canonical ensemble
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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. Gibbs called this themicrocanonicalensemble. In a system which can exchange energy at fixed temperature weaverage using the boltzmann factor of Eq.
This is the Maxwell-Boltzmann distribution which we have seen above for the ideal gas. Note that the interactions cancel out in numera-tor and demominator. Any classical system, gas, liquid, or solid (or polymer, glass, etc.) has this distribution for the momentum of any particle. 4.2.2. Boltzmann equipartition theorem
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