  We study a microscopically realistic model of a physical gel and use computer
simulations to investigate its static and dynamic properties at thermal
equilibrium. The phase diagram comprises a sol phase, a coexistence region
ending at a critical point, a gelation line, and an equilibrium gel phase
unrelated to phase separation. The global structure of the gel is homogeneous,
but the stress is supported by a fractal network. Gelation results in a
dramatic slowing down of the dynamics, which can be used to locate the
transition, which otherwise shows no structural signatures. Moreover, the
equilibrium gel dynamics is highly heterogeneous as a result of the presence of
particle families with different mobilities. An analysis of gel dynamics in
terms of mobile and arrested particles allows us to elucidate several
differences between the dynamics of equilibrium gels and that of glass-formers.
