  The difference between the zero-mass limit of the heat exchanged with a
thermal reservoir, and its value as determined from overdamped dynamics, is
termed `heat leakage' or `hidden heat' in the Smoluchowski limit. If present,
heat leakages are the sign of the unsuitability of the overdamped approximation
for addressing thermodynamics. It is accepted that no hidden heat arises in an
isothermal process driven by conservative forces. Here, we challenge that
conclusion. The heat exchanged with a reservoir in any isothermal and
quasistatic process connecting two equilibrium states, indeed exhibits hidden
contributions. Our results imply that the overdamped dynamics misrepresents
thermodynamics quite generally. Surprisingly, the hidden heat is described by
an universal distribution in slow processes, easing the correction of the heat
statistics in that context.
