**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31584

##### 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:**

**Keywords:**
Non-equilibrium,
lattice gas,
stochastic process

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

**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-V├ízquez 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.