Thermodynamic description of few-body systems How large should a system be to become thermal?
Thermodynamic description is well-established for systems with large numbers (say, of order of $N_A\sim 10^{23}$) of constituents. Is there a "lower bound" of sorts, for the number of degrees of freedom $N$ in a system, for which thermodynamic notions such as temperature, entropy, etc., still remain applicable?
Thank you!
 A: Check this link out:
Statistical mechanics of Henon-Heiles oscillator
It is shown that although the system has only 2 degrees of freedom, due to the non-linearity the system exhibits ergodic character, which is endemic of systems with large DoF.
A: As far as I see it, as it was mentioned in the previous answer - it's all about ergodicity. For example, if we consider a thermodynamic system of $N$ particles, the lower the number of particles in it, the bigger the fluctuations of some physical quantity $f$ ($\langle \Delta f^2 \rangle \sim N^{-1/2}$), and thus the bigger the relaxation time $\tau$ of the system to one of its stationary states. If $\tau$ is comparable with the characteristic time of physical measurements (i.e. the time, over which the averaging is performed), the time average can not equal to ansamble average (which is ergodicity in the simplest form).
Wrapping it up in a simple manner: if a mechanical system demonstrates congruent behavior in some bounded area of its phase space at fixed energy we can apply statistical mechanics formalism, and talk about ergodicity, however definitions of such thermodynamic quantities as temperature can have different meanings.
