  The classical Kubo-Martin-Schwinger (KMS) condition is a fundamental property
of statistical mechanics characterizing the equilibrium of infinite classical
mechanical systems. It was introduced in the seventies by G. Gallavotti and E.
Verboven as an alternative to the Dobrushin-Lanford-Ruelle (DLR) equation. In
this article, we consider this concept in the framework of nonlinear
Hamiltonian PDEs and discuss its relevance. In particular, we prove that Gibbs
measures are the unique KMS equilibrium states for such systems. Our proof is
based on Malliavin calculus and Gross-Sobolev spaces. The main feature of our
work is the applicability of our results to the general context of white noise,
abstract Wiener spaces and Gaussian probability spaces, as well as to
fundamental examples of PDEs like the nonlinear Schrodinger, Hartree, and wave
(Klein-Gordon) equations.
