PX284 - B2 - microstates and macrostates

microstate

any microscopic configuration of the system
eg: specify the position, and the velocity for every molecule in $1 l$ of gas
this is very difficult/impossible to measure

macrostate

any configuration with particular measurable properties
eg: specify internal energy $(U)$ , pressure $(p)$ , and volume $(V)$ for $1 l$ of gas
each macrostate can correspond to many microstates

example

3 simple harmonic oscillators (SHOs) with $E = 2 ℏ ω$ can be arranged in six ways, ignoring the zero point energy

\begin{matrix} \begin{matrix} 2 & 0 & 0 \end{matrix} & E^{(1)} = 2 ℏ ω \\ \begin{matrix} 1 & 1 & 0 \\ 1 & 0 & 1 \end{matrix} & E^{(2)} = ℏ ω \\ \begin{matrix} 0 & 1 & 1 \\ 0 & 0 & 2 \\ 0 & 2 & 0 \end{matrix} & E^{(3)} = 0 ℏ ω \end{matrix}

here, the total number of microstates: $Ω = 6$
if a measurement is done sensitive to:
- $E :$ there is $1$ macrostate
- $E^{(1)}$ (the energy of SHO 1): there are 3 macrostates: $E^{(1)} = (2 o r 1 o r 0) ℏ ω$ with 1, 2, and 3 microstates respectively