TY - JOUR

T1 - Revisiting Feynman's ratchet with thermoelectric transport theory

AU - Apertet, Y.

AU - Ouerdane, H.

AU - Goupil, C.

AU - Lecoeur, Ph

PY - 2014/7/15

Y1 - 2014/7/15

N2 - 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 analog 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 Î that quantifies the amount of heat that flows through the cold and hot sides of both heat engines. While it is well established that Î=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 Î=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.

AB - 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 analog 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 Î that quantifies the amount of heat that flows through the cold and hot sides of both heat engines. While it is well established that Î=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 Î=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.

UR - http://www.scopus.com/inward/record.url?scp=84905498384&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.90.012113

DO - 10.1103/PhysRevE.90.012113

M3 - Article

C2 - 25122257

AN - SCOPUS:84905498384

VL - 90

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1

M1 - 012113

ER -