We discuss the reversibility of Brownian heat engine. We perform asymptotic analysis of Kramers equation on Büttiker-Landauer system and show quantitatively that Carnot efficiency is inattainable even in a fully overdamping limit. The inattainability is attributed to the inevitable irreversible heat flow over the temperature boundary.PACS number: 05.10.Gg, 05.70.Ln, 87.10.+e How efficiently can Brownian heat engine work? This question is important not only for the construction of theory of molecular motors [1] but also for foundation of non-equilibrium statistical physics. Like Carnot cycle, Brownian heat engine can extract work from the difference of the temperature of heat baths, where Brownian working material operates as a transducer of thermal energy into mechanical work. The feature of this engine is: 1) It operates autonomously. 2) It is driven by finite difference of the temperature of heat baths both of which contact with the working material simultaneously. Thus, this engine works because the system is out of equilibrium. Feynman [2] devised what is called Feynman's ratchet that can rectify the thermal fluctuation for work using the difference of the temperature of two thermal baths. Büttiker [3] and Landauer [4] proposed a simpler type of Brownian motor and pointed out that one could extract work even by the simple heat engine where a Brownian particle is subject to a spatially periodic heat baths in a periodic potential [5].One crucial point on the Brownian engines is the efficiency [2,[6][7][8][9][10][11][12][13][14][15][16][17]. Feynman claimed that his thermal ratchet can operate reversibly, resulting in Carnot efficiency. Recently, however, some authors claimed that Feynman's claim was incorrect, while some author supported it: Parrondo and Español discussed that Feynman's ratchet should not work reversibly since the engine is simultaneously in contact with heat baths at different temperatures [6]. Sekimoto devised so-called "stochastic energetics" and applied it into Feynman's ratchet [7]. He showed numerically that the efficiency is much less than that of Carnot. Hondou and Takagi showed that reversible operation of Feynman's ratchet is impossible using reductio ad absurdum [10]. Magnasco and Stolovitzky studied how the engine generates motion with detailed analysis of its phase space [11]. On the other hand, Sakaguchi claimed that the Feynman's ratchet could operate reversibly by proposing a "stochastic boundary condition" [8]. Similar result is also found in ref. [15] (not on Feynman's ratchet but on Büttiker-Landauer system), on which detailed discussion will be made later. These studies have reminded us that there is difficulty as to the energetic description on Brownian systems, because naive application of conventional energetics formulated in thermodynamic and/or equilibrium system into Brownian system may lead incorrect result.Operation of Brownian engines is done by the engines themselves and the engines are, therefore, out of equilibrium. To clarify the non-equilibrium nature of B...

In the thermodynamic limit, the existence of a maximal efficiency of energy conversion attainable by a Carnot cycle consisting of quasi-static isothermal and adiabatic processes precludes the existence of a perpetual machine of the second kind, whose cycles yield positive work in an isothermal environment. We employ the recently developed framework of the energetics of stochastic processes (called 'stochastic energetics'), to re-analyze the Carnot cycle in detail, taking account of fluctuations, without taking the thermodynamic limit. We find that both in this non-macroscopic situation, both processes of connection to and disconnection from heat baths and adiabatic processes that cause distortion of the energy distribution are sources of inevitable irreversibility within the cycle. Also, the so-called null-recurrence property of the cumulative efficiency of energy conversion over many cycles and the irreversible property of isolated, purely mechanical processes under external 'macroscopic' operations are discussed in relation to the impossibility of a perpetual machine, or Maxwell's demon. This analysis may serve as the basis for the design and analysis of mesoscopic energy converters in the near future. 05.90+m, 05.40-a, 05.70-a, 02.50-r

We formulate energetics of the forced thermal ratchet [M. O. Magnasco, Phys. Rev. Lett. 71, 1477(1993] and evaluate its efficiency of energy transformation. We show that the presence of thermal fluctuation cannot increase the efficiency of the energy transformation in the original system of Magnasco, which is contrary to his claim that "There is a region of the operating regime where the efficiency is optimized at finite temperatures." We also discuss the maximum efficiency of the forced thermal ratchet. [S0031-9007(98)06408-4] PACS numbers: 05.40.+j, 87.10.+e Molecular motors are known to have the high efficiency of energy transformation even in the presence of thermal fluctuation [1]. Motivated by the interesting fact, recent studies of thermal ratchet models [2] are showing how work should be extracted from nonequilibrium fluctuations [3][4][5][6][7][8][9][10][11]. Fluctuation-induced work has been a subject not only for biological interest but also for the foundation of statistical physics: Thermal fluctuation-induced motion in ratchet systems were also investigated earlier [2][3][4].One of the important findings among ratchet models was by Magnasco [7] where he showed that the Brownian particle in periodic potential with broken symmetry, the so-called ratchet, can exhibit a nonzero net drift if the particle is subject to an external fluctuation having sufficient time correlation. He also studied the temperature dependence on the fluctuation-induced current in the system and showed that the current can be maximized at a finite temperature. This interesting finding has been interpreted that the existence of thermal fluctuation does not disturb the fluctuation-induced motion and even facilitates the efficiency of energy transformation.The latter claim is quite surprising, because thermal fluctuation is naively considered to disturb effective operation of a machine. In mesoscopic systems as in molecular motors, one cannot escape from the effect of thermal fluctuation. Therefore, Magnasco's finding has been followed and analyzed further by much literature (see references in Ref. [11]). We show, however, this interpretation is incorrect, by energetic analysis [12,13] of Magnasco's original system [7]. The efficiency of energy transformation is not maximized at finite temperature: The maximum efficiency is realized in the absence of thermal fluctuation. It turns out that the following problem has not yet been solved: Can thermal fluctuation facilitate the efficiency of energetic transformation from force fluctuation into work in general ratchet systems?Let us consider a forced ratchet system subject to an external load against global motion:where x represents the state of the ratchet, j͑t͒ is a thermal noise satisfying ͗j͑t͒j͑t 0 ͒͘ 2kTd͑t 2 t 0 ͒, "͗· · ·͘" is an operator of ensemble average, F͑t͒ is an external fluctuation with temporal period t, F͑t 1 t͒ F͑t͒, R t 0 dt F͑t͒ 0, and V L is a potential due to the load, ≠V L ≠x l . 0. The geometry of the potential, V ͑x͒ V 0 ͑x͒ 1 V L ͑x͒, is displayed in Fig.

Coherent motion is found to emerge out of fluctuations in a vibrated asymmetric particle. Depending on the parameters, amplitude, and frequency of the box, the motion of the particle is classified into several phases. The transition between fluctuating motion and unidirectional motion occurs with constant acceleration in the low-frequency regime and constant amplitude in the high-frequency regime. We show through dimensional analysis that this behavior does not depend on the detailed geometry of the particle.