An H-theorem for the general relativistic Ornstein-Uhlenbeck process

Journal of Mathematical Physics

Volumn 46, Issue 10, 2005, Pages

  Rigotti, M ^a,b   Debbasch, F ^a  

^a OBSERVATOIRE DE PARIS   (France)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27844449555     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2038627     Document Type: Article

References (29)

1. Barbachoux, C., Debbasch, F., and Rivet, J. P., " Covariant Kolmogorov equation and entropy current for the relativistic Ornstein-Uhlenbeck process., " Eur. Phys. J. B 23, 487 (2001).
2. Barbachoux, C., Debbasch, F., and Rivet, J. P., " The spatially one-dimensional relativistic Ornstein-Uhlenbeck process in an arbitrary inertial frame., " Eur. Phys. J. B 19, 37 (2001).
3. Beck, C. and Schloegl, F., Thermodynamics of Chaotic Systems, An Introduction (Cambridge University Press, Cambridge, 1993).
4. Boltzmann, L., Vorlesungen über Gastheorie, Erweiterter Nachruck der 1896-1898 bei Ambrosius Barth in Leipzig erschienen Ausgabe, 1981. Akademische Druck u. Verlagsanstalt, Graz.
5. de Groot, S. R., van Leeuwen, W. A., and van Weert, C. G., Relativistic Kinetic Theory (North-Holland, Amsterdam, 1980).
6. Debbasch, F., " A diffusion process in curved space-time., " J. Math. Phys. 45, 7 (2004).
7. Debbasch, F., Mallick, K., and Rivet, J. P., " Relativistic Ornstein-Uhlenbeck process., " J. Stat. Phys. 88, 945 (1997).
8. Debbasch, F. and Rivet, J. P., " A diffusion equation from the relativistic Ornstein-Uhlenbeck process., " J. Stat. Phys. 90, 1179 (1998).
9. Dunkel, J. and Hänggi, P., " Theory of relativistic Brownian motion: The (1+1) -dimensional case., " Phys. Rev. E 71, 016124 (2005).
10. Franchi, J. and le Jan, Y., " Relativistic diffusions and Schwarzschild geometry., " arXiv math.PR/0410485, 2004.
11. Grimmett, G. R. and Stirzaker, D. R., Probability and Random Processes, 2nd ed. (Oxford University Press, Oxford, 1994).
12. Hawking, S. W. and Ellis, G. F. R., The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 1973).
13. Huang, K., Statistical Machanics, 2nd ed. (Wiley, New York, 1987).
14. Israel, W., " Covariant fluid mechanics and thermodynamics: An introduction, " in Relativistic Fluid Dynamics., edited by, A. Anile, and, Y. Choquet-Bruhat, Lecture Notes in Mathematics, Vol. 1385 (Springer, Berlin, 1987).
15. Johnson, C. V., D-Branes (Cambridge University Press, Cambridge, 2003).
16. Jüttner, F., " Die relativistische quantentheorie des idealen gases., " Z. Phys. 47, 542-566 (1928).
17. Kaku, M., Introduction to Superstrings and M-theory, 2nd ed. (Springer, New York, 1999).
18. Kullback, S., Information Theory and Statistics (Wiley, New York, 1951).
19. Kullback, S. and Leibler, R. A., " On information and sufficiency., " Ann. Math. Stat. 22, 79-86 (1951).
20. Landau, L. D. and Lifshitz, E. M., The Classical Theory of Fields, 4th ed. (Pergamon, Oxford, 1975).
21. Landau, L. D. and Lifshitz, E. M., Fluid Mechanics (Pergamon, Oxford, 1987).
22. Mackey, M. C., Time's Arrow: The Origins of Thermodynamic Behavior (Springer, Berlin, 1992).
23. Øksendal, B., Stochastic Differential Equations, 5th ed. (Universitext. Springer, Berlin, 1998).
24. Truesdell, C. A., Rational Thermodynamics (Springer, New York, 1984).
25. van Kampen, N. G., Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
26. Voigt, J., " Stochastic operators, information, and entropy., " Commun. Math. Phys. 81, 31-38 (1981).
27. Wald, R. M., General Relativity (The University of Chicago Press, Chicago, 1984).
28. Wald, R. M., Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chicago Lectures in Physics (The University of Chicago Press, Chicago, 1994).
29. Wald, R. M., editor, Black Holes and Relativistic Stars (The University of Chicago Press, Chicago, 1998).