  The TRAPPIST-1 planetary system consists of seven planets within 0.05 au of
each other, five of which are in a multi-resonant chain. {These resonances
suggest the system formed via planet migration; subsequent tidal evolution has
damped away most of the initial eccentricities. We used dynamical N-body
simulations to estimate how long it takes for the multi-resonant configuration
that arises during planet formation to break. From there we use secular theory
to pose limits on the tidal parameters of planets b and c. We calibrate our
results against multi-layered interior models constructed to fit the masses and
radii of the planets, from which the tidal parameters are computed
independently.} The dynamical simulations show that the planets typically go
unstable 30 Myr after their formation. {Assuming synchronous rotation
throughout} we compute $\frac{k_2}{Q} \gtrsim 2\times 10^{-4}$ for planet b and
$\frac{k_2}{Q} \gtrsim 10^{-3}$ for planet c. Interior models yield
$(0.075-0.37) \times 10^{-4}$ for TRAPPIST-1 b and $(0.4-2)\times 10^{-4}$ for
TRAPPIST-1 c. The agreement between the {dynamical and interior} models is not
too strong, but is still useful to constrain the dynamical history of the
system. We suggest that this two-pronged approach could be of further use in
other multi-resonant systems if the planet's orbital and interior parameters
are sufficiently well known.
