  Controlled dephasing of electrons, via 'which path' detection, involves, in
general, coupling a coherent system to a current driven noise source. However,
here, we present a case in which a nearly isolated electron puddle at thermal
equilibrium strongly affects the coherence of a nearby electronic
interferometer. Moreover, for certain average electron occupations of the
puddle, the interferometer exhibits complete dephasing. This robust phenomenon
stems from the Friedel Sum Rule, which relates a system's occupation with its
scattering phases. The interferometer opens a peeping window into physics of
the isolated electron puddle, which cannot be accessed otherwise.
