# Statistical mechanics: What is a "microscopic realization" of a system?

What is a "microscopic realization" of a system?

The context is statistical mechanics. The microscopic system consists of many atoms (too many to track individually) with an assigned probability density function f(x,y,z,Vx,Vy,Vz,t).

The macroscopic system consists of the atoms taken together, with macroscopic quantities computed as expectations of microscopic quantities.

• Can you add some context? What's the paragraph preceding and following this sentence?
– BMS
Sep 3, 2014 at 9:03
• Added some context. Sep 3, 2014 at 9:27

Now, in the same way that when you cast a dice, a realization would be any number between 1 and 6 (for instance 3), then for a thermodynamic system with say fixed $(E,N,V)$, a microscopic realization can be any microstate compatible with these constraints (for instance all the particles in the corner of the box with one particle having all the energy $E$ of the system and the rest of the particles having no motion). You just have to imagine that you have in your hands a god like device that can tell you the instantaneous positions and velocities of all the particles in your system. Each time you perform a measurement with this device, you will be observing a microstate compatible with the statistical ensemble and hence observing a microscopic realization of this ensemble.