  We show how the formalism used for thermoelectric transport may be adapted to
Smoluchowski's seminal thought experiment also known as Feynman's ratchet and
pawl system. Our analysis rests on the notion of useful flux, which for a
thermoelectric system is the electrical current and for Feynman's ratchet is
the effective jump frequency. Our approach yields original insight into the
derivation and analysis of the system's properties. In particular we define an
entropy per tooth in analogy with the entropy per carrier or Seebeck
coefficient, and we derive the analogue to Kelvin's second relation for
Feynman's ratchet. Owing to the formal similarity between the heat fluxes
balance equations for a thermoelectric generator (TEG) and those for Feynman's
ratchet, we introduce a distribution parameter that quantifies the amount of
heat that flows through the cold and hot sides of both heat engines. While it
is well established that $\gamma$ = 1/2 for a TEG, it is equal to 1 for
Feynman's ratchet. This implies that no heat may be rejected in the cold
reservoir for the latter case. Further, the analysis of the efficiency at
maximum power shows that the so-called Feynman efficiency corresponds to that
of an exoreversible engine, with $\gamma$ = 1. Then, turning to the nonlinear
regime, we generalize the approach based on the convection picture and
introduce two different types of resistance to distinguish the dynamical
behavior of the considered system from its ability to dissipate energy. We
finally put forth the strong similarity between the original Feynman ratchet
and a mesoscopic thermoelectric generator with a single conducting channel.
