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- Summary:
- A microstate is one of possible states of the system common to a macrostate. In 6N dimensional phase space every point is a possible state, then what is the meaning of density of states?

Hello all. I am studying stat mech from Pathria's book.

It says a system is completely described by all positions and momenta of all the N particles. This maybe represented by a single point in 6N-D gamma space. So, each point is a (micro)state.

Now if we restrict the system (N,V,E to E+ΔE), the there is an allowed region in which microstates may exist.

In this region, every single point is a different state (in classical mech., there's no Planck's constant and unlimited precission.) So what's even the meaning of asking the distribution of states? It's like asking density of real numbers!

For every point in this space, either it is one of the allowed state or it is not. Even if there's a Planck's constant and limited precision, still this density can be either a finite constant or 0. It sounds digital to me.

Please help.

It says a system is completely described by all positions and momenta of all the N particles. This maybe represented by a single point in 6N-D gamma space. So, each point is a (micro)state.

Now if we restrict the system (N,V,E to E+ΔE), the there is an allowed region in which microstates may exist.

In this region, every single point is a different state (in classical mech., there's no Planck's constant and unlimited precission.) So what's even the meaning of asking the distribution of states? It's like asking density of real numbers!

For every point in this space, either it is one of the allowed state or it is not. Even if there's a Planck's constant and limited precision, still this density can be either a finite constant or 0. It sounds digital to me.

Please help.