Calculation of the Entropy Balance Equation in a Non-equilibrium Reaction-diffusion System

Entropy

Volumn 12, Issue 12, 2010, Pages 2436-2449

  Mahara, Hitoshi ^a   Yamaguchi, Tomohiko ^a  

^a NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

Author keywords

Entropy balance; Entropy balance equation; Entropy change; Entropy flow; Entropy production; Reaction diffusion system; Reversible Gray Scott model

Indexed keywords

EID: 80054994001     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e12122436     Document Type: Review

References (32)

1. Nicolis, G.; Prigogine, I. Self-Organization in Non-Equilibrium System; Wiley & Sons, Inc: New York, NY, USA, 1977; pp. 31–60.
2. Kondepudi, D. Introduction to Modern Thermodynamics; John Wiley & Sons, Ltd: Chichester,UK, 1998; pp. 239–357.
3. Kondo, S.; Asai, R. A viable reaction-diffusion wave on the skin of Pomacanthus, a marine angelfish. Nature 1995, 376, 765–768.
4. Martiel, J.L.; Goldbeter, A. A model based on receptor desensitization for cyclic AMP signaling in Dictyostelium cells. Biophys. J. 1987, 52, 807–828.
5. Gray, P.; Scott, S.K. Autocatalytic reactions in the isothermal continuous stirred-tank reactor: Oscillations and instabilities. Chem. Eng. Sci. 1984, 39, 1087–1097.
6. Field, R.J.; Noyes, R.M. Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction. J. Am. Chem. Soc. 1974, 96, 2001–2006.
7. J. P. Keener and J. J. Tyson, Spiral waves in the Belousov-Zhabotinskii reaction. Physica D 1986, 21, 307–324.
8. FitzHugh, R. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1961, 1, 445–466.
9. Pearson, J.E. Complex Patterns in a Simple System. Science 1993, 261, 189–192.
10. Lee, K.J.; McCormick, W.D.; Ouyang, Q.; Swinney, H.L. Pattern formation by interacting chemical fronts. Science 1993, 261, 192–194.
11. De Kepper, P.; Castets, V.; Dulos, E.; Boissonade, J. Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction. Physica D 1991, 49, 161–169.
12. Epstein, I.R.; Pojman, J.A. An Introduction to Nonlinear Chemical Dynamics—Oscillations, Waves, Patterns and Chaos; Oxford University Press: New York, NY, USA, 1998; pp. 1–450.
13. Vanag, V.K.; Epstein, I.R. Pattern Formation in a Tunable Medium: The Belousov-Zhabotinsky Reaction in an Aerosol OT Microemulsion. Phys. Rev. Lett. 2001, 87, 228301.
14. Mahara, H.; Suzuki, K.; Jahan, R.A.; Yamaguchi, T. Coexisting stable patterns in a reaction-diffusion system with reversible Gray-Scott dynamics. Phys. Rev. E 2008, 78, 066210.
15. Nishiura, Y.; Teramoto, T.; Ueda, K.-I. Scattering of traveling spots in dissipative systems. Chaos 2005, 15, 047509.
16. Glansdorff, P.; Prigogine, I. Sur les proprietes differentielles de la production d’entropie. Physica 1954, 20, 773–780.
17. Sawada, Y. A thermodynamic variational principle in nonlinear non-equilibrium phenomena. Prog. Theor. Phys. 1981, 66, 68–76.
18. Shimizu, H.; Sawada, Y. Relative stability among metastable steady state structures in chemical reaction systems. J. Chem. Phys. 1983, 79, 3828–3835.
19. Hill, A. Entropy production as the selection rule between different growth morphologies. Nature 1990, 348, 426–428.
20. Martiouchev, L.M.; Seleznev, V.D.; Kuznetsova, I.E. Application of the principle of maximum entropy production to the analysis of the morphological stability of a growing crystal. J. Exp. Theor. Phys. 2000, 91, 132–143.
21. Shimokawa, S.; Ozawa, H. Thermodynamics of irreversible transitions in the oceanic general circulation. Geophys. Res. Lett. 2007, 34, L12606.
22. Paltridge, G.W.; Farquhar, G.D.; Cuntz, M. Maximum entropy production, cloud feedback, and climate change. Geophys. Res. Lett. 2007, 34, L14708.
23. Jones, W. Variational principles for entropy production and predictive statistical mechanics. J. Phys. A Math. Gen. 1983, 16, 3629–3634.
24. Dewar, R. Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states. J. Phys. A Math. Gen. 2003, 36, 631–641.
25. Dewar, R.C. Maximum entropy production and the fluctuation theorem. J. Phys. A: Math. Gen. 2005, 38, L371–L381.
26. Irvin, B.R.; Ross, J. Calculation of the rate of entropy production for a model chemical reaction. J. Chem. Phys. 1988, 89, 1064–1066.
27. Ishida, K.; Matsumoto, S. Non-equilibrium thermodynamics of temporally oscillating chemical reactions. J. Theoret. Biol. 1975, 52, 343–363.
28. Hanson, M.P. Spatial structures in dissipative systems. J. Chem. Phys. 1974, 60, 3210–3214.
29. Mahara, H.; Suematsu, N.J.; Yamaguchi, T.; Ohgane, K.; Nishiura, Y.; Shimomura, M. Three-variable reversible Gray-Scott model. J. Chem. Phys. 2004, 121, 8968–8972.
30. Mahara, H.; Yamaguchi, T.; Shimomura, M. Entropy production in a two-dimensional reversible Gray-Scott system. Chaos 2005, 15, 047508.
31. Mahara, H.; Yamaguchi, T. Entropy balance in distributed reversible Gray-Scott model. Physica D 2010, 239, 729–734.
32. Munteanu, A.; Solé, R.V. Pattern formation in noisy self-replicating spots. Int. J. Bifurcation Chaos 2006, 16, 3679–3685.