Effective temperature and compactivity of a lattice gas under gravity

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 4, 2002, Pages 3-

  Sellitto, Mauro ^a  

^a ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY (SPECIFIC GRAVITY); FUNCTIONS; GRANULAR MATERIALS; GRAVITATION; INTEGRAL EQUATIONS; LATTICE VIBRATIONS; THERMODYNAMICS;

LATTICE GASES; MEAN-SQUARE DISPLACEMENT; THERMAL VIBRATIONS; THERMODYNAMIC EQUILIBRIUM;

GAS DYNAMICS;

ARTICLE;

EID: 37649027128     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.042101     Document Type: Article

References (19)

1. L.F. Cugliandolo, J. Kurchan, and L. Peliti, Phys. Rev. E 55, 3898 (1997).
2. S. Franz and M.A. Virasoro, J. Phys. A 33, 891 (2000).
3. A. Barrat, J. Kurchan, V. Loreto, and M. Sellitto, Phys. Rev. Lett. 85, 5034 (2000).
4. S.F. Edwards, in Granular Matter: An Interdisciplinary Approach, edited by A. Mehta (Springer-Verlag, Berlin, 1994).
5. W. Kob and H.C. Andersen, Phys. Rev. E 48, 4364 (1993).
6. Notice that there is no purely horizontal motion in a bcc lattice: any elementary (one lattice spacing) displacement is either upward or downward.
7. M. Sellitto and J.J. Arenzon, Phys. Rev. E 62, 7793 (2000).
8. Y. Levin, Europhys. Lett. 55, 767 (2001);J.J. Arenzon et al. (unpublished).
9. M. Sellitto, Phys. Rev. E 63, 060301 (2001).
10. J.J. Arenzon (private communication).
11. A. Barrat, V. Colizza, and V. Loreto, Phys. Rev. E 66, 011310 (2002).
12. M.H. Vainstein and J.J. Arenzon (unpublished).
13. L. Peliti and M. Sellitto, J. Phys. (France) 8, 49 (1998);
14. The evolution of the density profile is detailed in M. Sellitto, J. Phys.: Condens. Matter 14, 1455 (2002).
15. This is indeed suggested by the functional nature of the nonzero gravity lattice gas entropy. For example, in the noninteracting case, Hamiltonian Eq. (1), the equilibrium entropy is (Formula presented)From the minimization of the free energy one then gets (Formula presented)
16. J. Berg, S. Franz, and M. Sellitto, Eur. Phys. J. B 26, 349 (2002).
17. A. Lefèvre, e-print cond-mat/0202376.
18. The occurrence of a first order phase transition in the Edwards measure of the KA model was pointed out to me by S. Franz. For a study of dynamical heterogeneities in the same model, see S. Franz, R. Mulet, and G. Parisi, Phys. Rev. E 65, 021506 (2002).
19. Notice that in the inhomogeneous case—when the entropy is a functional of the density profile, the functional version of Eq. (7) holds, and (Formula presented) will only depend on the density profile provided its thermodynamic interpretation holds true.