Efficiency at maximum power of Feynman's ratchet as a heat engine

The maximum power of Feynman's ratchet as a heat engine and the corresponding efficiency (η ∗ ) are investigated by optimizing both the internal parameter and the external load. When a perfect ratchet device (no heat exchange between the ratchet and the pawl via kinetic energy) works between two thermal baths at temperatures T 1 > T 2 , its efficiency at maximum power is found to be η ∗ = η 2 C /[η C − (1 − η C )ln(1 − η C )], where η C ≡ 1 − T 2 / T 1 . This efficiency is slightly higher than the value obtained by Curzon and Ahlborn (1975 Am. J. Phys. 43 22) for macroscopic heat engines. It is also slightly larger than the result η SS ≡ 2η C /(4 − η C ) obtained by Schmiedl and Seifert (2008 EPL 81 20003) for stochastic heat engines working at small temperature differences, while the evident deviation between η ∗ and η SS appears at large temperature differences. For an imperfect ratchet device in which the heat exchange between the ratchet and the pawl via kinetic energy is non-vanishing, the efficiency at maximum power decreases with increase in the heat conductivity.