  Blazar S5 0716+714 is well-known for its short-term variability, down to
intra-day time-scales. We here present the 2-min cadence optical light curve
obtained by the TESS space telescope in 2019 December - 2020 January and
analyse the object fast variability with unprecedented sampling. Supporting
observations by the Whole Earth Blazar Telescope Collaboration in B, V , R, and
I bands allow us to investigate the spectral variability during the TESS
pointing. The spectral analysis is further extended in frequency to the UV and
X-ray bands with data from the Neil Gehrels Swift Observatory. We develop a new
method to unveil the shortest optical variability time-scales. This is based on
progressive de-trending of the TESS light curve by means of cubic spline
interpolations through the binned fluxes, with decreasing time bins. The
de-trended light curves are then analysed with classical tools for time-series
analysis (periodogram, auto-correlation and structure functions). The results
show that below 3 d there are significant characteristic variability
time-scales of about 1.7, 0.5, and 0.2 d. Variability on time-scales < 0.2 d is
strongly chromatic and must be ascribed to intrinsic energetic processes
involving emitting regions, likely jet sub-structures, with dimension less than
about milliparsec. In contrast, flux changes on time-scales > 0.5 d are
quasi-achromatic and are probably due to Doppler factor changes of geometric
origin.
