  The soliton resolution conjecture is one of the most interesting open
problems in the theory of nonlinear dispersive equations. Roughly speaking it
asserts that a solution with generic initial condition converges to a finite
number of solitons plus a radiative term. In this paper we use the complexity
of a finite object, a notion introduced in Algorithmic Information Theory, to
show that the soliton resolution conjecture is equivalent to the analogous of
the second law of thermodynamics for the complexity of a solution of a
dispersive equation.
