Undergrad Evolution of a Boltzman distribution

[kelly0303]

Hello! Assume I have a classical system at a fixed temperature, such that the energy can be described by a Boltzmann distribution at that temperature. If I have a huge number of such systems in that state, and I measure the energy of each one, independently, the probability of measuring a given energy would reach the Boltzmann distribution (in the limit of a large number of measurements). However, if I measure the energy of a system to be $E_1$ and a time $t$ later I measure the same system, and I repeat that many times, would I still get a Boltzmann distribution. My question here is in the classical case, I am not talking about wavefunction collapse (also the way you measure the energy shouldn't be important either). My question mainly is, are the measurements correlated, such that for a given time interval between measurements, the probability of the second measurement depends on the value of the first one?

 

[hutchphd]

Just a point of nomenclature: you are worrying about the difference between an ensemble average and a time average for a random process. For a discreet random process (say a coin toss) the two are equivalent I think . There are clearly many nuances here, which is why I offer you the nomenclature for further study...and bow out..

 

[DrClaude]

One of the major assumptions of statistical physics is that for a system at equilibrium, ensemble average = time average. This is often referred to as the ergodic theorem.