Abstract
Coupled diffusion processes model the systems of molecular motors, in which chemical free energy is converted to mechanical energy. Entropy production rate is a crucial term in calculating the efficiency of the motors. In this paper, we calculate the entropy production rates of coupled diffusion processes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Astumian, R.D.: Thermodynamics and kinetics of a Brownian motor. Science 276, 917–923 (1997)
Bier, M., Astumian, R.D.: Biasing Brownian motion in different directions in a 3-state fluctuating potential and an application for the separation of small particles. Phys. Rev. Lett. 76, 4277–4280 (1996)
Chen, Z.Q., Zhao, Z.: Switched diffusion processes and systems of elliptic equations—a Dirichlet space approach. Proc. R. Soc. Edinb. A 124, 673–701 (1994)
Chung, K.L.: Lectures from Markov Processes to Brownian Motion. Springer, New York (1982)
Freidlin, M.: Markov Processes and Differential Equations: Asymptotic Problems. Birkhäuser, Zürich (1996)
Graham, C.: Nonlinear limit for a system of diffusing particles which alternate between two states. Appl. Math. Optim. 22, 75–90 (1990)
Jiang, D.Q., Qian, M., Qian, M.P.: Mathematical Theory of Nonequilibrium Steady States—On the Frontier of Probability and Dynamical Systems. Springer, Berlin (2004)
Jülicher, F., Ajdari, A., Prost, J.: Modeling molecular motors. Rev. Mod. Phys. 69, 1269–1281 (1997)
Magnasco, M.O.: Forced thermal ratchets. Phys. Rev. Lett. 71, 1477–1481 (1993)
Magnasco, M.O.: Molecular combustion motors. Phys. Rev. Lett. 72, 2656–2659 (1994)
Parmeggiani, A., Jülicher, F., Ajdari, A., Prost, J.: Energy transduction of isothermal ratchets: Generic aspects and specific examples close to and far from equilibrium. Phys. Rev. E 60, 2127–2140 (1999)
Peskin, C.S., Ermentrout, G.B., Oster, G.F.: In: Mow, V., et al. (eds.) Cell Mechanics and Cellular Engineering, pp. 476–489. Springer, New York (1994)
Pinsky, M.: Lectures on Random Evolution. World Scientific, Singapore (1991)
Prost, J., Chauwin, J.F., Peliti, L., Ajdari, A.: Asymmetric pumping of particles. Phys. Rev. Lett. 72, 2652–2655 (1994)
Qian, M., Zhang, B.: Multi-dimensional coupled diffusion process. Acta Math. Appl. Sin. 1, 168–179 (1984)
Qian, M., Zhang, F.: Entropy production rate of the minimal diffusion process. Acta Sci. Math. 27B, 145–152 (2007)
Qian, M., Wang, Y., Zhang, X.J.: Stochastic resonance and ratches: two closely related phenomena in Brownian motors. Chin. Phys. Lett. 20, 810–812 (2003)
Qian, M., Zhang, X., Wilson, R.J., Feng, J.: Efficiency of Brownian motors in terms of entropy production rate. Europhys. Lett. 84, 10014 (2008)
Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361, 57–265 (2002)
Xi, F.: Asymptotic properties of jump-diffusion processes with state-dependent switching. Stoch. Process. Appl. 119, 2198–2221 (2009)
Yildiz, A., Tomishige, M., Vale, R.D., Selvin, P.R.: Kinesin walks hand-over-hand. Science 303, 676–678 (2004)
Zhang, F.: Ergodicity and reversibility of the minimal diffusion process. Markov Process. Relat. Fields 11, 661–676 (2005)
Zhou, H.X., Chen, Y.D.: Chemically driven motility of a Brownian particles. Phys. Rev. Lett. 77, 194–197 (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Qian, M., Zhang, F. Entropy Production Rate of the Coupled Diffusion Process. J Theor Probab 24, 729–745 (2011). https://doi.org/10.1007/s10959-011-0352-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10959-011-0352-9