The Directed Transport And Nonequilibrium Thermodynamic Analysis Of Three Typical Brownian Motors

Once we know the initial and final energies of the system and the path between them, the work output of the system can be determined by classical thermodynamics.In fact, there exists the quantity of fluctuations with k_BT dominate in the energies of the two states and the exchange heat between the system and the environment.In the Boltzmann statistic the quantity of fluctuations is usually negligible.However,the fluctuations aren't negligible as the systems are very small.The statistical thermodynamic issues appearing in microscopic systems are becoming the holdback which has to be faced with in the nano science.Molecular motors are just such microscopic systems which may serve as the basis for physicists to solve the problems.The phenomenon of noise induced directed transport has attracted much interest in recent years.It has widespread applications in physics,chemistry and biology.One particular system which has been intensively studied both theoretically and experimentally is the motion of motor proteins like kinesins or dyneins.These motor proteins are responsible for the transport of cell organelles along the cytosceleton.They move randomly but directly on average and have been modeled by Brownian ratchets,and consequently,the concept of Brownian motors has been used to illuminate the directed, noise-induced transport.Based on the above reasons,this thesis is focused on the discussion of several typical Brownian models,and then the directed transports of Brownian motors are investigated. The performance parameters of the thermally driven Brownian motors systems under the influence of the irreversibilities are searched by using nonequilibrium thermodynamics. The main research contents are organized as follows:The brief introduction of the dynamics theory of the Brownian motion and thermodynamic ratchets and Brownian motors are given.The research histories, classification,construction of the model and theory frame of the molecular motors are presented in detail.The insufficiency of the Brownian ratchet model in existence is explored and analyzed.It is expected that this discussion can give some inspire for future research.The transport of Brownian particles in two-state flashing ratchets composed of two asymmetric potentials with the same period is investigated.The analytic expression of a probability current is derived by using the power series expansion method and used to generate the curve characteristics of the current varying with other parameters.The effects of the asymmetric parameters and heights of two potentials and the transition rates between two states on the probability current are discussed in detail.It is found that the current is affected by not only the asymmetric parameters and heights of two potentials but also the transition rates between two states.It is also found that the heights of two potentials may change the magnitude as well as the direction of the current when the transition rates between two states are not the same. Based on a general model of Brownian motors,the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically.It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion.Only when the heat leak in the system is negligible,can the determinant of the Onsager matrix vanish.Moreover,the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail.The characteristic curves of the generalized efficiency varying with these parameters are presented.The maximum generalized efficiency and the corresponding optimum parameters are determined.The results obtained here are of general significance.They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with the zero heat leak,zero average drift velocity or linear response relation.An equivalent cycle system is established based on the above discussion and the Onsager coefficients and efficiency at the maximum power output of the system are analytically calculated from nonequilibrium thermodynamics.It is found that the Onsager reciprocity relation holds and the Onsager coefficients are affected by the main irreversibilities existing in practical systems.Only when the heat leak and the kinetic energy change of the particle in the system are negligible,can the determinant of the Onsager matrix vanish.It is also found that in the frame of nonequilibrium thermodynamics,the power output and efficiency of an irreversible Brownian motor can be expressed to be the same form as those of an irreversible Carnot heat engine,so the results obtained here are of general significance.Moreover,these results can be used to analyze the performance characteristics of a class of thermally driven Brownian motors.On the basis of the double-well potential which can be calculated theoretically and implemented experimentally,the influence of the time delay,number of particles and asymmetric parameter of the potential on the performance of a delayed feedback ratchet is investigated.The center-of-mass velocity of Brownian particles,the average effective diffusion coefficient and Pe number are calculated.It is expounded that the parameters are affected by not only the time delay and number of particles but also the asymmetric parameter of the double-well ratchet potential.It is very interesting to find that the current transport reversal may be obtained by varying the number of particles of the system.It is expected that the results obtained here may be observed in some physical and biological systems because the double-well ratchet potential is realizable experimentally.The results obtained in the thesis may provide some theoretical bases for the deep investigation on the three classes of typical Brownian motors mentioned above as well as some references for the optimal design of some relevant nano machines.