  We endow a system of interacting particles with two distinct, local,
Markovian and reversible microscopic dynamics. Using common field-theoretic
techniques used to investigate the presence of a glass transition, we find that
while the first, standard, dynamical rules lead to glassy behavior, the other
one leads to a simple exponential relaxation towards equilibrium. This finding
questions the intrinsic link that exists between the underlying,
thermodynamical, energy landscape, and the dynamical rules with which this
landscape is explored by the system. Our peculiar choice of dynam- ical rules
offers the possibility of a direct connection with replica theory, and our
findings therefore call for a clarification of the interplay between replica
theory and the underlying dynamics of the system.
