We usually say that temperature is related to the average kinetic energy of the particles in a system. That makes sense statistically, but it makes me wonder what temperature actually means at the microscopic level. Suppose I isolate a single atom in a perfect vacuum. It has some velocity and therefore some kinetic energy, but can I meaningfully say that the atom has a temperature? And if temperature is fundamentally a property of an ensemble rather than an individual particle, where exactly does the transition happen between “a collection of particles with individual energies” and “a system with a well-defined temperature”? For example, if I had only two particles, could I assign a temperature to them in any physically meaningful way? What about ten particles, a hundred, or a thousand? Is there a precise physical or statistical reason why temperature becomes a meaningful quantity only when the number of degrees of freedom becomes sufficiently large, or is “temperature” just an emergent macroscopic description that we choose because it is useful? I'm particularly interested in whether there is a fundamental lower limit on the size of a system for which temperature can be defined, rather than just a practical experimental limitation.