[bkcooper]

This is false. A single particle can still be described by the maximum entropy probability distribution given its average energy . . .

I'm not sure that construction makes sense. For a single particle not interacting with anything, imposing the maxent constraint on average energy just sets the energy of the particle and there's no room left for a distribution. As soon as its interacting with another system you're good, but then the temperature that you arrive it is a characteristic of the bath, not the particle itself.

[asafira]

how does the average energy set the energy of the particle?

To me, for any configuration of the particle x, the average energy of the particle is given by

sum over all configurations of p(x) E(x)

and there's the probability distribution over configurations.

[alecst]

I think what the OPs mean is that in the classical case, the lone, noninteracting particle has a fixed, definite energy and not an average energy. There are no other configurations to consider, besides the set of points that the particle may be in space, but that is irrelevant to the energy and temperature. Maybe what you're saying is true if you consider a single quantum particle, I'm not sure.

[evanb]

I think the issue is that, assuming the particle is alone or only elastically bouncing off of its container, E(x) is a constant E in which case (let's assume no internal degrees of freedom) the configuration contains only position and orientation information, rather than any information about a spread in energies.

edit: sniped by alecst.