Some states have been discovered which do not (see below), and their reasons for not reaching thermal equilibrium are unclear as of March 2019[update].
Systems with many interacting constituents are generally expected to be chaotic, but this assumption sometimes fails.
A notable counter example is the Fermi–Pasta–Ulam–Tsingou problem, which displays unexpected recurrence and will only thermalise over very long time scales.
[6] Non-chaotic systems which are pertubed by weak non-linearities will not thermalise for a set of initial conditions, with non-zero volume in the phase space, as stated by the KAM theorem, although the size of this set decreases exponentially with the number of degrees of freedom.
[7] Many-body integrable systems, which have an extensive number of conserved quantities, will not thermalise in the usual sense, but will equilibrate according to a generalized Gibbs ensemble.