Easy rhythms and melodies

Abstract

In the previous chapter we laid the foundations of statistical mechanics, whichstand on the fundamental Boltzmann postulate. However, the “Smaller Vehicle”provided by the microcanonical distribution is of little use to tackle practical problems, even when very simple. While discussing the ideal gas, we have indeed seen that selecting all and only those microstates that have a given value of the energy requires a tremendous effort. Therefore, we would like to find a way to avoid this “selection” task, which in almost all cases turns out to be a kind of “mission impossible”. What follows shows that this can easily be achieved by considering a system in thermal equilibrium with a reservoir.

“What, never?” “No, never!”

“What, never?” “Well, hardly ever!”

Gilbert & Sullivan, H.M.S. Pinafore

(also, The Simpsons, season 5, episode 2: Cape Feare)