Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Non-equilibrium Statistical Mechanics of a Driven Lattice Gas Model: Probability Function, FDT-violation, and Monte Carlo Simulations

Authors: K. Sudprasert, M. Precharattana, N. Nuttavut, D. Triampo, B. Pattanasiri, Y. Lenbury, W. Triampo

Abstract:

The study of non-equilibrium systems has attracted increasing interest in recent years, mainly due to the lack of theoretical frameworks, unlike their equilibrium counterparts. Studying the steady state and/or simple systems is thus one of the main interests. Hence in this work we have focused our attention on the driven lattice gas model (DLG model) consisting of interacting particles subject to an external field E. The dynamics of the system are given by hopping of particles to nearby empty sites with rates biased for jumps in the direction of E. Having used small two dimensional systems of DLG model, the stochastic properties at nonequilibrium steady state were analytically studied. To understand the non-equilibrium phenomena, we have applied the analytic approach via master equation to calculate probability function and analyze violation of detailed balance in term of the fluctuation-dissipation theorem. Monte Carlo simulations have been performed to validate the analytic results.

Keywords: Non-equilibrium, lattice gas, stochastic process

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071860

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1333

References:


[1] J. W. Dufty and J. Lutsko, Recent Developments in Non-equilibrium Thermodynamics, J. Casas-Vazques, D. Jou and J. M. Rubi, Ed. Berlin: Springer, 1986.
[2] J. Krug and H. Spohn, Solids Far from Equilibrium: Growth, Morphology and Defects, C. Godreche, Ed. New York: Cambridge University Press, 1991.
[3] G. Nicolis and I. Prigogine, Self-Organization in Non-equilibrium Systems. New York: Wiley, 1977.
[4] R. Bhattacharya and M. Majumdar,,Random dynamical systems and chaos: Theory and Application, Cambridge: Cambridge University Press, 2007, pp.119-239.
[5] S. Perrett, S. J. Freeman, P. J. G. Butler and A. R., "Equilibrium folding properties of the yeast prion protein determinant Ure2", J. Mol. Biol., vol. 290, no. 1, pp. 331-345, Jul. 1999.
[6] J. Wong-ekkabut, W. Triampo, I.-Ming Tang, D. Triampo, D. Baowan, and Y. Lenbury, "Vacancy-Mediated Disordering Process in Binary Alloys at Finite Temperatures: Monte Carlo Simulations", J. Korean Phys. Soc., vol. 45, 2003.
[7] Bar-Yam Yaneer, Dynamical of Complex Systems, Boston: Addison- Wesley,1997,.pp.38-57.
[8] E. Ben-Naim, H. Frauenfelder, Z. Toroczkai, Complex Networks, Berlin: Springer, 2004,. pp. 51-88
[9] R. Ash, Information theory, New York: Wiley, 1965, pp.169-210.
[10] J. Avery, Information Theory and Evolution, Toh Tuck Lin: World Scientific, 2003
[11] Econophysics and Sociophysics, B. K. Chakrabarti, A. Chakraborti, and A. Chatterjee, Ed. New York: WILEY-VCH, 2006,.pp. 65-88.
[12] P. C. Martin and J. Schwinger, "Theory of many-particle systems. I". Phys. Rev., vol. 115, no. 6, pp. 1342 - 1373, Mar. 1959.
[13] J.-P. Eckmann and I. Procaccia, "Onset of defect-mediated turbulence". Phys. Rev. Lett., vol. 66, no. 7, pp. 891-894, May. 1991.
[14] J. Casas-Vázquez and D. Jou, "Nonequilibrium temperature versus localequilibrium temperature", Phys. Rev. E, vol. 49, no. 2, pp. 1040 - 1048, Aug. 1994.
[15] A. Campos and BL. Hu, "Nonequilibrium dynamics of a thermal plasma in a gravitational field". Phys. Rev. D, vol. 58, no. 12, pp. 125021, Feb. 1998.
[16] D. Boyanovsky, F. Cooper, H. J. de Vega, and P. Sodano, "Evolution of inhomogeneous condensates: Self-consistent variational approach". Phys. Rev. D, vol. 58, pp. 025007, Feb. 1998.
[17] G. Torrieri, S. Jeon, and J. Rafelski, "Particle yield fluctuations and chemical nonequilibrium in Au-Au collisions at sqrt
[s_ {NN}]= 200 GeV", Phys. Rev. C, vol. 74, no. 2, pp. 024901, Feb. 2006.
[18] W. Kwak, Y. Jae-Suk, K. In-mook, and D. P. Landau, "Sub-block order parameter in a driven Ising lattice gas using block distribution functions", Phys. Rev. E, vol. 75, no. 4, pp. 041108, Nov. 2007.
[19] J. Honerkamp, Stochastic Dynamical Systems: Concepts, Numerical Methods, Data Analysis. New York: VCH. , 1994.
[20] M. Blume, V. J. Emery, and Robert B. Griffiths, "Ising Model for the Transition and Phase Separation in He^{3}-He^{4} Mixtures", Phys. Rev. A, vol. 4, no. 3, pp. 1071-1077, Mar. 1971.
[21] P. C. Hohenberg and B. I. Halperin, "Theory of dynamic critical phenomena", Rev. Mod. Phys., vol. 49, no. 3, pp. 435-479, Jul. 1977.
[22] K. G. Wilson, "The renormalization group: Critical phenomena and the Kondo problem", Rev. Mod. Phys., vol. 47, no. 4, pp. 773-840, Jul. 1975.
[23] B. Schmittmann and R. K. P. Zia, Statistical Mechanics of Driven Diffusive Systems , C. Domb and J. L. Lebowitz, Ed. New York: Academic Press, 1995.
[24] S. Katz, J. Lebowitz, H. Spohn, "Phase transitions in stationary nonequilibrium states of model lattice systems", Phys. Rev. B, vol. 28, no. 3, pp. 1655-1658, Dec. 1983.
[25] K. G. Wilson, "The renormalization group and critical phenomena ", Rev. Mod. Phys., vol. 55, no. 3, pp.583-600, Jul. 1983.
[26] R. R. Netz and A. Aharony, "Critical behavior of energy-energy, strainstrain, higher-harmonics, and similar correlation functions", Phys. Rev. E, vol. 55, no. 3, pp. 2267-2278, Aug. 1997.
[27] Y. Chen, "Short-time critical behavior of anisotropic cubic systems", Phys. Rev. B, vol. 63, no. 9, pp. 092301, Sep. 2001.
[28] J. Marro, J. L. Vallés, and J. M. Gonz├ílez-Miranda, "Critical behavior in nonequilibrium phase transitions", Phys. Rev. B, vol. 35, no. 7, pp. 3372- 3375, Jul. 1987.
[29] I. Svare, F. Borsa, D. R. Torgeson, and S. W. Martin, "Correlation functions for ionic motion from NMR relaxation and electrical conductivity in the glassy fast-ion conductor (Li_ {2} S) _ {0.56}(SiS_ {2}) _ {0.44}", Phys. Rev. B, vol. 48, no. 13, pp. 9336-9344, Mar. 1993.
[30] S. Adams and J. Swenson, "Determining ionic conductivity from structural models of fast ionic conductors", Phys. Rev. Lett., vol. 84, no. 18, pp. 4144-4147, Sep. 2000.
[31] N. Metropolis, A.W. Rosenbluth, M.M. Rosenbluth, A.H. Teller and E. Teller, "Equation of state calculations by fast computing machines", J. Chem. Phys., vol. 21, no. 6, pp.1087, Mar. 1953.
[32] F. Spitzer, "Interaction of Markov processes", Adv. Math., vol. 5, no. 2, pp. 246-290, 1970.
[33] R.K.P. Zia and T. Blum, Scale Invariance, Interfaces, and Nonequilibrium Dynamics, A. Mckane et al., Ed. New York: Plenum Press, 1995.
[34] W. Triampo, I.M. Tang, J. Wong-Ekkabut, "Explicit Calculations on Small Non-Equilibrium Driven Lattice Gas Models", J. Korean Phys. Soc., vol. 43, no. 2, pp. 207-214, 2003.
[35] L. Onsager, " Crystal statistics. I. A two-dimensional model with an order-disorder transition", Phys. Rev., vol. 65, no. 3-4, pp.117-149, Oct. 1944.
[36] L.P. Kadanoff, "Critical Phenomena", Proceedings of International School of Physics "Enrico Fermi,", Course 51, M. S. Green, Ed. New York: Academic, 1971.