Thermodynamics and complexity of simple transport phenomena

Journal of Physics A: Mathematical and General

Volumn 39, Issue 6, 2006, Pages 1311-1338

  Jepps, Owen G ^a   Rondoni, Lamberto ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31344440018     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/39/6/007     Document Type: Article

References (43)

1. Khinchin A I 1949 Mathematical Foundations of Statistical Mechanics (New York: Dover)
2. Gallavotti G 1999 Statistical Mechanics: A Short Treatise (Berlin: Springer)
3. Gallavotti G and Cohen E G D 1995 Dynamical ensembles in stationary states J. Stat. Phys. 80 931
4. Gaspard P 1998 Chaos, Scattering and Statistical Mechanics (Cambridge: Cambridge University Press)
5. Evans D J, Searles D J and Rondoni L 2005 Application of the Gallavotti-Cohen fluctuation relation to thermostated steady states near equilibrium Phys. Rev. E 71 056120
6. Li B, Casati G and Wang J 2003 Heat conductivity in linear mixing systems Phys. Rev. E 67 021204
7. Alonso D, Ruiz A and de Vega I 2004 Transport in polygonal billiards Physica D 187 184
8. Artuso R, Casati G and Guarneri I 1997 Numerical study on ergodic properties of triangular billiards Phys. Rev. E 55 6384
9. Casati G and Prosen T 1999 Mixing properties of triangular billiards Phys. Rev. Lett. 83 4729
10. Gutkin E 2003 Billiard dynamics: a survey with the emphasis on open problems Regular Chaotic Dyn. 8 1
11. Artuso R and Cristadoro G 2003 Weak chaos and anomalous transport: a deterministic approach Commun. Nonlinear Sci. Numer. Simul. 8 137
12. Artuso R 1997 Anomalous diffusion in classical dynamical systems Phys. Rep. 290 37-47
13. Gutkin E 1986 Billiards in polygons Physica D 19 311
14. Galerpin G, Krüger T and Troubetzkoy S 1995 Local instability of orbits in polygonal and polyhedral billiards Commun. Math. Phys. 169 463
15. Cecconi F, del Castillo-Negrete D, Falcioni M and Vulpiani A 2003 The origin of diffusion: the case of non-chaotic systems Physica D 180 129
16. Dettmann C P, Cohen E G D and van Beijeren H 1999 Microscopic chaos from brownian motion? Nature 401 875
17. Lepri S, Rondoni L and Benettin G 2000 The Gallavotti-Cohen fluctuation theorem for a nonchaotic model J. Stat. Phys. 99 857
18. Benettin G and Rondoni L 2001 A new model for the transport of particles in a thermostated system Math. Phys. Electron. J. 7 3
19. Jepps O G, Bhatia S K and Searles D J 2003 Wall mediated transport in confined spaces: exact theory Phys. Rev. Lett. 91 126102
20. Sanders D P and Larralde Hernán 2005 Occurrence of normal and anomalous diffusion in polygonal billiard channels Preprint cond-mat/0510654
21. Troubetzkoy S 1998 Complexity lower bounds for polygonal billiards Chaos 8 242
22. Gutkin E and Tabachnikov S 2004 Complexity of piecewise convex transformations, with applications to polygonal billiards Preprint math.DS/0412335
23. Lloyd J, Niemeyer M, Rondoni L and Morriss G P 1995 The nonequilibrium Lorentz gas Chaos 5 536
24. Harayama T, Klages R and Gaspard P 2002 Deterministic diffusion in flower shape billiards Phys. Rev. E 66 026211
25. Koza Z 2004 Fractal dimension of transport coefficients in a deterministic dynamical system J. Phys. A: Math. Gen. 37 10859-77
26. Klages R and Dorfman J R 1995 Simple maps with fractal diffusion coefficients Phys. Rev. Lett. 74 387-90
27. Klages R and Dellago Ch 2000 Density-dependent diffusion in the periodic Lorentz gas J. Stat. Phys. 101 145-59
28. Chernov N I, Eyink G L, Lebowitz J L and Sinai Ya G 1993 Steady state electric conductivity in the periodic Lorentz gas Commun. Math. Phys. 154 569
29. Chernov N I, Eylink G L, Lebowitz J L and Sinai Ya G 1993 Derivation of Ohm's law in a deterministic mechanical model Phys. Rev. Lett. 70 2209-12
30. Chernov N 2001 Sinai billiards under small external forces Ann. Henri Poincaré 2 197-236
31. Sotta P, Lesne A and Victor J M 2000 The coil-globule transition for a polymer chain confined in a tube: a Monte Carlo simulation J. Chem. Phys. 113 6966-73
32. Gutkin E 1996 Billiards in polygons: survey of recent results J. Stat. Phys. 83 7
33. de Groot S R and Mazur P 1984 Non-Equilibrium Thermodynamics (New York: Dover)
34. Chapman S and Cowling T G 1970 The Mathematical Theory of Non-Uniform Gases (Cambridge: Cambridge University Press)
35. Falcioni M and Vulpiani A 2004 private communication
36. Boffetta G, Cencini M, Falcioni M and Vulpiani A 2002 Predictability: a way to characterize complexity Phys. Rep. 356 367
37. Korabel N and Klages R 2002 Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems Phys. Rev. Lett. 89 214102
38. Ott Edward 1993 Chaos in Dynamical Systems (Cambridge: Cambridge University Press)
39. Fermi E 1956 Thermodynamics (New York: Dover)
40. Reichl L E 1984 A Modern Course in Statistical Physics (Austin, TX: University of Texas Press)
41. Kittel C and Kroemer H 1980 Thermal Physics (San Francisco: Freeman)
42. Cohen E G D and Rondoni L 2002 Particles, maps and irreversible thermodynamics Physica A 306 117
43. Rondoni L and Cohen E G D 2002 On some derivations of irreversible thermodynamics from dynamical systems theory Physica D 168-169 341