] 2 5 M ar 1 99 8 Efficiency of Brownian Motors

The efficiency of different types of Brownian motors is calculated analytically and numerically. We find that motors based on flashing ratchets present a low efficiency and an unavoidable entropy production. On the other hand, a certain class of motors based on adi-abatically changing potentials, named reversible ratchets, exhibit a higher efficiency and the entropy production can be arbitrarily reduced. In the last years there has been an increasing interest in the so-called " ratchets " or Brownian motors [1, 2, 3, 4, 5, 6]. These systems consist of Brownian particles moving in asymmetric potentials, such as the one depicted in fig. 1 (left), and subject to a source of non-equilibrium, like external fluctuations or temperature gradients. As a consequence of these two ingredients —asymmetric potentials and non-equilibrium—, a flow of particles can be induced. Most of the cited papers consider systems where the Brownian particles do not gain energy in a systematic way. Although these systems are called " Brownian or molecular motors " , they do not convert heat into work, nor induce any energy conversion. Feynman in his Lectures [7] already understood that, in order to have an engine out of a ratchet, it is necessary to use its systematic motion to store potential energy. This can be achieved if the ratchet lifts a load. Then the ratchet becomes a thermal engine and Feynman estimated its efficiency (although following assumptions which have been revealed to contain some inconsistencies [8]). Recently, Sekimoto [9] has generalized this procedure, defining efficiency for a wide class of ratchets. Jülicher et al [6] have also discussed the efficiency of molecular motors and Sokolov and Blumen [10] have calculated the efficiency of a deterministically flashing ratchet in contact with thermal baths at different temperatures. A general conclusion is that these motors are intrinsically irreversible, even in the quasistatic limit [6, 8, 9, 10]. On the other hand, it has been recently introduced [11] a class of deterministically driven ratchets where the entropy production vanishes in the quasistatic limit, i.e., reversible ratchets. The aim of this letter is to explore the differences, regarding efficiency, between randomly flashing ratchets and both reversible and irreversible deterministically driven ratchets. Randomly flashing ratchets Consider two species of Brownian particles, say A and B, moving in the interval [0, L] with periodic boundary conditions. Particles of type A feel a potential V A (x), whereas particles B feel V B …