  We study a certain type of the celebrated Fermi-Pasta-Ulam particle chain,
namely the inverted FPU model, where the inter-particle potential has a form of
a quartic double well. Numerical evidence is given in support of a simple
symbolic description of dynamics (in the regime of sufficiently high potential
barrier between the wells) in terms of an (approximate) Markov process. The
corresponding transition matrix is formally identical to a ferromagnetic
Heisenberg quantum spin-1/2 chain with long range coupling, whose
diagonalization yields accurate estimates for a class of time correlation
functions of the model.
