The Investigation On The Thermodynamic Performance Of The Thermally-driven Brownian Motors

In recent years, the research on the transport of Brownian particle driven by fluctuation in periodic structure system has become the foreland problem of the non-equilibrium statistical physics. Brownian motor is a nanometer scale machine and an asymmetric structure in space. The transport of Brownian particles is driven by some non-equilibrium processes, such as external load force, chemical potential difference, temperature difference, et al. When the system is completely in the environment of thermal fluctuations, the Brownian motor becomes the most basic heat engine model. The Brownian motor can integrate thermal fluctuations and do useful work. In this thesis, the two kind of the Brownian motors driven by temperature difference are studied. The heat engine model can be constructed by a spatial period temperature field and sawtooth potential as well as in the one-dimensional lattice. We analyze the thermodynamic property of the Brownian heat engine and explore the influence of the irreversible factors on the thermodynamic property in the Brownian heat engine model.In chapter I, we briefly introduce the development of statistical physics. The theoretical basis of Brownian motion is the Brownian dynamic theory and it has become the important content of the non-equilibrium statistical physics. Meanwhile, we introduce the research situation of the Brownian heat engine at domestic and aboard and the main research content of this paper.In chapter II, the Brownian heat engine driven by temperature difference in a periodic double-barrier sawtooth is investigated. Brownian particles move in the periodic double-barrier sawtooth potential with an external load force and contact with an alternating hot and cold reservoir. The dynamic property of particles is described by the Fokker-Planck equation. The kinetic energy of the Brownian particles and the heat leak between hot and cold reservoir are considered simultaneously. The influence of the main parameters, including the height of barrier, the ratio of the low barrier to high barrier and the external load force, on the efficiency and power output of Brownian heat engine is discussed in detail. In chapter III, the influence of the heat reservoir boundary on the thermodynamic property of a thermal Brownian heat engine in a periodic single-barrier sawtooth is analyzed. We change the heat reservoir distribution in the Feynman-Smoluchowski heat engine model. The steady-state current, efficiency and power output of the heat engine are derived analytically based on Fokker-Planck equation. The influence of the heat reservoir boundary on the efficiency and power output of heat engine is discussed. It is shown that the efficiency of the engine will enhance but the power output will reduce when we change the heat reservoir boundary.In chapter IV, we model a Feynman’s ratchet and pawl heat engine in a one-dimensional lattice. The dynamic property of particles in the lattice is described by the master equation. The influence of the main parameters, including the height of barrier, the ratio of the low barrier to high barrier and the external load force, on the heat current, efficiency and power output of Brownian heat engine is discussed in detail. It is shown that an irreversible heat leak exists in the system. The Feynman’s ratchet and pawl heat engine is an irreversible heat engine and the efficiency is far lower than the Carnot efficiency.