= Solution
A <thermoelectric generator> maintains hot and cold junctions of two materials with different <Seebeck coefficients>. Mobile charge carriers redistribute in the <temperature gradient>, producing an open-circuit <voltage> of magnitude $|V|=|S_p-S_n|\Delta T$ for constant coefficients. A load permits <electric current>; pairs of p-type and n-type legs are commonly connected electrically in series and thermally in parallel. Maintaining the output requires continuous <heat transfer> from the hot reservoir and rejection of <heat> to the cold reservoir. The <thermoelectric figure of merit> $ZT=S^2\sigma T/\kappa$ expresses the favorable combination of large <Seebeck coefficient>, large <electrical conductivity> and small <thermal conductivity>. Contact losses, Joule heating and parasitic <heat> leaks reduce practical efficiency.
A <pyroelectric generator> instead exploits a change of spontaneous <electric polarization> with <temperature>. If the relevant component of the <pyroelectric coefficient> is $p=dP_s/dT$, an <electrode> of area $A$ receives a short-circuit <electric current> approximately $I=pA\,dT/dt$. A heating stroke and a cooling stroke produce opposite charge changes. Rectification or a synchronized electrical cycle can transfer <energy> to storage. \b[A spatial <temperature> difference drives the thermoelectric device; a temporal <temperature> change drives the pyroelectric device.] Uniform, constant <temperature> gives no continuing current from <pyroelectricity> even if the material is hot. Reported nanowire generators deliberately use changing <temperature>, rather than infer continuous generation from a static hot specimen.<Pyroelectric nanogenerators for harvesting thermoelectric energy by Ya Yang and others>[Nano Letters 12 (2012), pp.2833–2838, transient-temperature operating principle]{ref}
Both approaches can be compact, silent and free of macroscopic moving parts. The <thermoelectric generator> gives continuous output under a sustained gradient, but needs two effective thermal contacts and sufficient <heat> flow; very small $\Delta T$ gives a small <voltage> and thermal contacts can consume much of the available gradient. Thin films exhibiting <pyroelectricity> can respond to intermittent heating without a permanently maintained hot/cold separation across their thickness, but require repeated thermal cycling, low electrical leakage and suitable charge extraction. Their thermal <time constant> limits useful cycling <frequency>, and sensible heating/cooling can dominate the <heat> budget. A steady hot pipe with an available cold sink favors a <thermoelectric generator>; periodic radiative heating can favor a <pyroelectric generator>. Neither converts equilibrium thermal motion at a single fixed <temperature> into sustained useful <work>.
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