I am studying some quantum mechanics and thermodynamics. I have seen that in QM temperature doesn't appears in the formulas. But it appears in statistical mechanics formulas.
The question is: Temperature appears as a phaenomena of a big number of particles? How big must be that number?
EDIT
I have seen the link Can a single molecule have a temperature? but there is no agreement on the answers. So, this question might be Can a single molecule have a temperature? revisited
For a single particle to have a defined instantaneous temperature is ... unlikely.
Maybe a polymerized blob (vulcanized auto tire?) can have particle character and lots of internal energetic degrees of freedom, and have a temperature that a thermometer could measure. It's a very big molecule, but perhaps still a 'single particle'.
A point particle kinetic energy does NOT define a temperature, in the absence of a stationary reference. Synchrotron beam particles can be ultrarelativistic, but are still cold (or the beam wouldn't be stable). Random motion of those particles is thermal, the velocity of the bunch is not.
A single particle might be at equilibrium with liquid helium, but be inside a fast-moving container. Randomness matters.
That's to some degree a matter of interpretation and definition.
You yourself have notice so much (on your remark about conflicting answers in the question this one is duplicate of). Even if attributing a temperature to a single molecule is at best a rough approximation, there might be circumstances where it's consistent and useful.
Another example of "lack of agreement" is whether it makes sense to talk about two different temperatures in plasmas: the electron temperature and the ion temperature. The electrons among themselves are in equilibrium, as are the ions among themselves, but the equilibration between both groups happens in a longer time scale, so in practice these temperatures are used in plasma physics, but many deem it inappropriate, as temperature would be defined only in (full?) equilibrium.
Temperature actually corresponds to the root mean square velocity of the collection of particles. If the there is only one particle, then the root mean square velocity is just the velocity of that single particle. So, we can say that even a single particle can possess certain temperature depending on its velocity.
Usually we see the change in temperature of two objects into thermal equilibrium as the statistical probability. The heat exchange between these two object tend to the highest multiplicity (the thermal equilibrium) and the higher the number of molecules, the higher the multiplicity too.
