C B Muratov 2001 J. Phys. A: Math. Gen. 34 4641 doi:10.1088/0305-4470/34/22/305
C B Muratov
Show affiliationsWe obtain an exact equation for a smoothed phase space distribution function for a system of N non-relativistic particles of unit mass obeying Hamiltonian dynamics. We show that this equation is well posed in only one time direction in the sense of the continuous dependence of the solution on the initial data. We interpret the ill-posedness of this equation in the backward time direction as the manifestation of irreversibility of the observable statistical quantities for systems obeying time-reversible dynamical laws.
65F22 Ill-posedness, regularization
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
Issue 22 (8 June 2001)
Received 7 December 2000, in final form 9 April 2001
C B Muratov 2001 J. Phys. A: Math. Gen. 34 4641
Takayoshi Sano and James M. Stone 2003 ApJ 586 1297
Jeremy F. Sepinsky et al. 2002 ApJ 574 937
W. Kley and D. N. C. Lin 1999 ApJ 518 833
C E Krauss et al 2003 New J. Phys. 5 70
R. P. Schiavon et al. 1997 ApJ 479 902
Steven Johnston 2008 Class. Quantum Grav. 25 202001
Jin Gyu Park et al 2007 Nanotechnology 18 405306
Werner Kaminsky et al 2010 J. Phys.: Condens. Matter 22 095902
P S Wong et al 2008 Nanotechnology 19 435710