  Thermoelectric energy conversion is a direct but low-efficiency process,
which precludes the development of long-awaited wide-scale applications. As a
breakthrough permitting a drastic performance increase is seemingly out of
reach, we fully reconsider the problem of thermoelectric coupling enhancement.
The corner stone of our approach is the observation that heat engines are
particularly efficient when their operation involves a phase transition of
their working fluid. We derive and compute the thermoelastic coefficients of
various systems, including Bose and Fermi gases, and fluctuation Cooper pairs.
Combination of these coefficients yields the definition of the thermodynamic
figure of merit, the divergence of which at $finite$ temperature indicates that
conditions are fulfilled for the best possible use of the thermoelectric
working fluid. Here, this situation occurs in the fluctuation regime only, as a
consequence of the increased compressibility of the working fluid near its
phase transition. Our results and analysis clearly show that efforts in the
field of thermoelectricity can now be productively directed towards systems
where electronic phase transitions are possible.
