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.
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