Determining the range of validity of this thermodynamics is not a simple problem.
Krylov (1944) suggested that the property of mixing was
at the heart of the this question.
Quick (exponential) mixing leads to a short relaxation time. It results in strongly chaotic behaviour (positive Lyapunov exponent).
However, one can also have slower (power-law) mixing processes that are weakly chaotic.
The difference emerges because of short (long) ranged interactions and smooth (complex i.e. fractal/multifractal) boundary conditions.
Krylov N.
1944. Nature 153, 709.