# Is ensemble a set of all microstates of a system?

Definition of ensemble says it's a collection of identical mental copies of a system in which microscopic parameters can differ.

Now, the phase space of the $$N$$ particles in the system in 3 dimensional physical contains all possible positions and momenta, $$\{q,p\}$$ of those particles in that system. So, can we think of each point in phase space as a microstate of the system?

Then geometrically ensemble is the phase space, right? I am very confused about how ensembles and microstates are connected.

• "microstates of a system" yes for microcanonical ensemble and technically yes for canonical essemble, but it always felt a bit strange since in canonical essemble the separability was assumed. The phase space was a bit out of context, the point of S.M. was to "simplify", which used extrinsic or intrinsic quantities, such as volume or temperature, to describe the system. So the variables here were more like energy e.t.c. than a point in the space. Even though doing calculations for things like a thermal engine, it's an integral over "fluid" rather than lots of moving balls scattering around. Aug 8, 2021 at 4:44

An ensemble is a conceptual tool required to provide a base for assigning probabilities to the microstates. In a frequentistic approach, the probability coincides with the frequency of an event. Ensembles are there just to provide a way to speak about the frequency of every single microstate. It is clear that in the phase space points are unique: a single microstate appears only once. In order to have more occurrences of the same state, one introduces this concept of $$N$$ mental copies of the system. If a microstate appears $$n$$ times, it will have a probability $$n/N$$.