  We describe the long-term evolution of compact systems of terrestrial
planets, using a set of simulations that match the statistical properties of
the observed exoplanet distribution. The evolution is driven by tidal
dissipation in the planetary interiors, but the systems evolve as a whole due
to secular gravitational interactions. We find that, for Earth-like dissipation
levels, planetary orbits can be circularised out to periods of order 100 days,
an order of magnitude larger than is possible for single planets. The resulting
distribution of eccentricities is a qualitative match to that inferred from
transit timing variations, with a minority of non-zero eccentricities
maintained by particular secular configurations. The coupling of the tidal and
secular processes enhance the inward migration of the innermost planets in
these systems, and can drive them to short orbital periods. Resonant
interactions of both the mean motion and secular variety are observed, although
the interactions are not strong enough to drive systemic instability in most
cases. However, we demonstrate that these systems can easily be driven unstable
if coupled to giant planets on longer period orbits.
