Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.
Sign up to join this community
We have read the Fundamental postulate of statistical mechanics which says that :
In a state of thermal equilibrium, All the accessible microstates of the system are equally probable.
Suppose a system in thermal equilibrium with total energy to be $E$. Now as every microstate is equally probable, Is the state in which all the energy is possessed by one particle is equally probable than other states? If yes, Why this isn't seen very often?
Because the macrostate is what you observe. Each macrostate is associated to a set o microstates. The probability of observing a macrostate is the sum of the probabilities of the equally likely microstates. Having all the particles at a single energy level has only one possibility. But having the particles spread over several energy levels gives rise to several microstates that correspond to a single macrostate.
For example, if you have 5 particles and you find a way to put them in a single energy level, then you have only one microstate and one macrostate.
However, if you find a way to put 3 particles in one energy level and 2 in another, then you have
$$\frac{5!}{3!2!}$$
different ways of doing this. All these different ways are microstates but macroscopically they are the same. So observing on of these states is much more probable.
note: I am assuming you are talking about distinguishable particles here.
