  We study the dynamical evolution of the TRAPPIST-1 system under the influence
of orbital circularization through tidal interaction with the central star. We
find that systems with parameters close to the observed one evolve into a state
where consecutive planets are linked by first order resonances and consecutive
triples, apart from planets c, d and e, by connected three body Laplace
resonances. The system expands with period ratios increasing and mean
eccentricities decreasing with time. This evolution is largely driven by tides
acting on the innermost planets which then influence the outer ones. In order
that deviations from commensurability become significant only on $Gy$ time
scales or longer, we require that the tidal parameter associated with the
planets has to be such that $Q' > \sim 10^{2-3}.$ At the same time, if we start
with two subsystems, with the inner three planets comprising the inner one,
$Q'$ associated with the planets has to be on the order (and not significantly
exceeding) $10^{2-3}$ for the two subsystems to interact and end up in the
observed configuration. This scenario is also supported by modelling of the
evolution through disk migration which indicates that the whole system cannot
have migrated inwards together. Also in order to avoid large departures from
commensurabilities, the system cannot have stalled at a disk inner edge for
significant time periods. We discuss the habitability consequences of the tidal
dissipation implied by our modelling, concluding that planets d, e and f are
potentially in habitable zones.
