Thermodynamics and Fluctuations Far From Equilibrium

Entropy

Volumn 12, Issue 10, 2010, Pages 2199-2243

  Ross, John ^a   Villaverde, Alejandro Fernández ^b  

^a STANFORD UNIVERSITY   (United States)

^b INSTITUTO DE INVESTIGACIONES MARINAS   (Spain)

Author keywords

Chemical reactions; Diffusion in chemical reaction kinetics; Irreversible thermodynamics; Nonequilibrium thermodynamics; Stochastic processes

Indexed keywords

EID: 79955026977     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e12102199     Document Type: Review

References (68)

1. Ross, J. Thermodynamics and Fluctuations Far from Equilibrium; Springer: Berlin, Germany, 2008.
2. Van Kampen, N.G. Stochastic Processes in Physics and Chemistry; North-Holland: Amsterdam, The Netherlands, 1981.
3. Ross, J.; Hunt, K.L.C.; Hunt, P.M. Thermodynamics far from equilibrium: Reactions with multiple stationary states. J. Chem. Phys. 1988, 88, 2719–2729.
4. Schlögl, F. On thermodynamics near a steady state. Z. Phys. 1971, 248, 446–458.
5. Evans, D.J.; Searles, D.J.; Williams, S.R. On the fluctuation theorem for the dissipation function and its connection with response theory. J. Chem. Phys. 2008, 128, 014504.
6. Glansdorff, P.; Nicolis, G.; Prigogine, I. The thermodynamic stability theory of non-equilibrium states. Proc. Natl. Acad. Sci. U. S. A. 1974, 71, 197–199.
7. Peng, B.; Hunt, K.L.C.; Hunt, P.M.; Suárez, A.; Ross, J. Thermodynamic and stochastic theory of nonequilibrium systems: Fluctuation probabilities and excess work. J. Chem. Phys. 1995, 102, 4548–4562.
8. Oppenheim, I.; Shuler, K.E.; Weiss, G.H. Stochastic Processes in Chemical Physics: The Master Equation; MIT: Cambridge, MA, USA, 1977.
9. Gardiner, C.W. Handbook of Stochastic Methods; Springer: New York, NY, USA, 1990.
10. Nicolis, G.; Babloyantz, A. Fluctuations in open systems. J. Chem. Phys. 1969, 51, 2632–2637.
11. Selkov, E.E. Self-oscillations in glycolysis. J. Biochem. 1968, 4, 79–86.
12. Graham, R.; Tél. T. Nonequilibrium potential for coexisting attractors. Phys. Rev. A 1986, 33, 1322–1337.
13. Maier, R.S.; Stein, D.L. Transition-rate theory for nongradient drift fields. Phys. Rev. Lett. 1992, 69, 3691–3695.
14. Crandall, M.G; Evans, L.C.; Lions, P.L. Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations. Trans. AMS 1984, 282, 487–502.
15. Jauslin, H.R. Nondifferentiable potentials for nonequilibrium steady states. Physica A 1987, 144, 179–191.
16. Jauslin, H.R. Melnikov's criterion for nondifferentiable weak-noise potentials. J. Stat. Phys. 1986, 42, 573–585.
17. Freidlin, M.I.; Wentzell, A.D. Random Perturbations of Mechanical Systems; Springer: Berlin, Germany, 1984.
18. Chu, X.; Ross, J.; Hunt, P.M.; Hunt, K.L.C. Thermodynamic and stochastic theory of reaction-diffusion systems with multiple stationary status. J. Chem. Phys. 1993, 99, 3444–3454.
19. Hansen, N.F.; Ross, J. Lyapunov functions and relative stability in reaction-diffusion systems with multiple stationary states. J. Phys. Chem. 1996, 100, 8040–8043.
20. Hansen, N.F.; Ross, J. Relative stability of multiple stationary states related to fluctuations. J. Phys. Chem. 1998, 102, 7123–7126.
21. Glauber, R.J. Lectures in Theoretical Physics; Interscience Publishing: New York, NY, USA, 1959.
22. Noyes, R.M.; Field, R.J.; Thompson, R.C. Mechanism of reaction of bromine (V) with weak one-electron reducing agents. J. Am. Chem. Soc. 1971, 93, 7315–7316.
23. Foerster, Y.-X.; Zhang, J.; Ross, J. Experiments on relative stability in the bistable multivariable bromate-ferroin reaction. J. Phys. Chem. 1993, 97, 4708–4713.
24. Bar-Eli, K; Geiseler, W. Mixing and relative stabilities of pumped stationary states. J. Phys. Chem. 1981, 85, 3461–3468.
25. Wolff, A.N.; Hjelmfelt, A.; Ross, J.; Hunt, P.M. Tests of thermodynamic theory of relative stability in one-variable systems. J. Chem. Phys. 1993, 99, 3455–3460.
26. Harding, R.H.; Ross, J. Experimental measurement of the relative stability of two stationary states in optically bistable ZnSe interference filters. J. Chem. Phys. 1990, 92, 1936–1946.
27. Lamb, H. Hydrodynamics, 6th ed.; Dover Publications: New York, NY, USA, 1945.
28. Saltzman, B. Finite amplitude free convection as an initial value problem-I. J. Atmos. Sci. 1962, 19, 329–341.
29. Lorenz, E.N. Deterministic nonperiodic flow. J. Atmos. Sci. 1963, 20, 130–141.
30. Getling, A.V. Rayleigh-Bénard Convection. Structure and Dynamics; World Scientific Pub. Co.: London, UK, 1997.
31. Glansdorff, P.; Prigogine, I. Thermodynamic Theory of Structure, Stability, and Fluctuations; Wiley: New York, NY, USA, 1971.
32. Keizer, J. Statistical Thermodynamics of Nonequilibrium Processes; Springer-Verlag: New York, NY, USA, 1987.
33. Attard, P. The second entropy: A general theory for non-equilibrium thermodynamics and statistical mechanics. Annu. Rep. Prog. Chem. Sect. C Phys. Chem. 2009, 105, 63–173
34. Ronis, D.; Procaccia, I. Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium. Phys. Rev. A 1982, 26, 1812–1815.
35. Fox, R.F. Gaussian stochastic processes in physics. Phys. Rep. 1978, 48, 179–283.
36. Velarde, M.G.; Chu, X.-L.; Ross, J. Toward a thermodynamic theory of hydrodynamics: The Lorenz equations. Phys. Fluids. 1994, 6, 550–563.
37. Zamora, M.; Rey de Luna, A. Energy of a system formed by a convective fluid and its container. J. Fluid Mech. 1986, 167, 427–437.
38. Law, B.M.; Sengers, J.V. Fluctuations in fluids out of thermal equilibrium. J. Stat. Phys. 1989, 57, 531–547.
39. Law, B.M.; Segrè, P.N.; Gammon, R.W.; Sengers, J.V. Light-scattering measurements of entropy and viscous fluctuations in a liquid far from thermal equilibrium. Phys. Rev. A 1990, 41, 816–824.
40. Segrè, P.N.; Gammon, R.W.; Sengers, J.V.; Law, B.M. Rayleigh scattering in a liquid far from thermal equilibrium. Phys. Rev. A 1992, 45, 714–724.
41. Li, W.B.; Segrè, P.N.; Gammon, R.W.; Sengers, J.V. Small-angle Rayleigh scattering from nonequilibrium fluctuations in liquids and liquid mixtures. Physica A 1994, 204, 399–435.
42. Suárez, A.; Ross, J. Thermodynamic and stochastic theory of coupled transport processes: Rayleigh scattering in a fluid in a temperature gradient. J. Phys. Chem. 1995, 99, 14854–14863.
43. Ross, J.; Chu, X.-L. Thermodynamic and stochastic theory for nonideal systems far from equilibrium. J. Chem. Phys. 1993, 98, 9765–9770.
44. Berry, R.S.; Rice, S.A.; Ross, J. Physical Chemistry, 2nd ed.; Oxford University Press: New York, NY, USA, 2000.
45. Keizer, J.; Chang, O.-K. The nonequilibrium electromotive force. I. Measurements in a continuously stirred tank reactor. J. Chem. Phys. 1987, 87, 4064–4073.
46. Keizer, J. The nonequilibrium electromotive force. II. Theory for a continuously stirred tank reactor. J. Chem. Phys. 1987, 87, 4074–4087.
47. Keizer, J. Thermodynamics at isothermal, isobaric steady states: vapor pressure, colligative properties, and the electromotive force. J. Phys. Chem. 1989, 93, 6939–6943.
48. Keizer, J. Heat, work, and the thermodynamic temperature at non-equilibrium steady states. J. Chem. Phys. 1985, 82, 2751–2771.
49. Field, R.J.; Burger, M. Oscillations and Traveling Waves in Chemical Systems; Wiley: New York, NY, USA, 1985.
50. Hjelmfelt, A.; Ross, J. Electrochemical experiments on thermodynamics at nonequilibrium steady states. J. Phys. Chem. 1994, 98, 9900–9902.
51. Hjelmfelt, A.; Ross, J. Kinetic and thermodynamic information derived from electrochemical measurements on stationary states. J. Phys. Chem. B 1998, 102, 3441–3444.
52. Ross, J.; Hunt, K.L.C.; Vlad, M.O. Determination of thermodynamic and stochastic potentials in non-equilibrium system from macroscopic measurements. J. Phys. Chem. A 2002, 106, 10951–10960.
53. Ross, J.; Hunt, K.L.C.; Hunt, P. Thermodynamics and stochastic theory for non-equilibrium systems with multiple reactive intermediates: The concept and role of excess work. J. Chem. Phys. 2002, 96, 618–629.
54. Kramer, J.; Ross, J. Stabilization of unstable states, relaxation, and critical slowing down in a bistable system. J. Chem. Phys. 1985, 83, 6234–6241.
55. Prigogine, I. Moderation et transformations irreversibles des systemes ouverts. Bull. Cl. Sci., Acad. R. Belg. 1945, 31, 600–606.
56. Ross, J.; Vlad, M.O. Exact solutions for the entropy production rate of several irreversible processes. J. Phys. Chem. A 2005, 109, 10607–10612.
57. Martyushev, L.M.; Seleznev,V.D. Maximum entropy production principle in physics, chemistry, and biology. Phys. Rep. 2006, 426, 1–45.
58. Lazar, J.G.; Ross, J. Changes in mean concentration, phase shifts, and dissipation in a forced oscillatory reaction. Science 1990, 247, 189–192.
59. Lax, M. Fluctuations in a nonequilibrium stable state. Rev. Mod. Phys. 1960, 32, 25–64.
60. Lax, M. Classical noise III: Nonlinear markoff processes. Rev. Mod. Phys. 1966, 38, 359–379.
61. Lax, M. Classical noise IV: Langevin methods. Rev. Mod. Phys. 1966, 38, 541–566.
62. Reif, F. Fundamentals of Statistical and Thermal Physics; McGraw-Hill: New York, NY, USA, 1965; Chapters 1, 15.
63. Chandrasekhar, S. Stochastic Problems in Physics and Astronomy. Rev. Mod. Phys. 1943, 15, 1–89.
64. Vlad, M.O.; Ross, J. Fluctuation-dissipation relations for chemical systems far from equilibrium. J. Chem. Phys. 1994, 100, 7268–7278.
65. Vlad, M.O.; Ross, J. Random paths and fluctuation-dissipation dynamics for one-variable chemical systems far from equilibrium. J. Chem. Phys. 1994, 100, 7279–7294.
66. Vlad, M.O.; Ross, J. Thermodynamic approach to nonequilibrium chemical fluctuations. J. Chem. Phys. 1994, 100, 7295–7309.
67. Nicolis, G.; Prigogine, I. Self-organization in Nonequilibrium Systems; Wiley: New York, NY, USA, 1977.
68. Tolman, R.C. The Principles of Statistical Mechanics; Oxford University Press: London, UK, 1938.