17 research outputs found
Irreversible Circulation of Fluctuation and Entropy Production
Physical and chemical stochastic processes described by the master equation
are investigated. In this paper, we examine the entropy production both for the
master equation and for the corresponding Fokker-Planck equation. For the
master equation, the exact expression of the entropy production was recently
derived by Gaspard using the Kolmogorov-Sinai entropy ({\em J.Stat.Phys.},
\textbf{117} (2004), 599; [Errata; \textbf{126} (2006), 1109 ]). Although
Gaspard's expression is derived from a stochastic consideration, it should be
noted that Gaspard's expression conincides with the thermodynamical expression.
For the corresponding Fokker-Planck equation, by using the detailed imbalance
relation which appears in the derivation process of the fluctuation theorem
through the Onsger-Machlup theory, the entropy production is expressed in terms
of the {\em irreversible circulation of fluctuation}, which was proposed by
Tomita and Tomita ({\em Prog.Theor.Phys.}, \textbf{51} (1974), 1731). However,
this expression for the corresponding Fokker-Planck equation differs from that
of the entropy production for the master equation. This discrepancy is due to
the difference between the master equation and the corresponding Fokker-Planck
equation, namely the former treats discrete events, but the latter equation is
an approximation of the former one. In fact, in the latter equation, the
original discrete events are smoothed out. To overcome this difficulty, we
propose the {\em path weight principle}. By using this principle, the modified
expression of the entropy production for the corresponding Fokker-Planck
equation coincides with that of the master equation (i.e., the thermodynamical
expression) for a simple chemical reaction system and a diffusion system.Comment: 17pages, no figures, to appear in Progreess of Theoretical Physics,
Vol. 119, No.
The Steady State Distribution of the Master Equation
The steady states of the master equation are investigated. We give two
expressions for the steady state distribution of the master equation a la the
Zubarev-McLennan steady state distribution, i.e., the exact expression and an
expression near equilibrium. The latter expression obtained is consistent with
recent attempt of constructing steady state theormodynamics.Comment: 6 pages, No figures. A mistake was correcte
Classical Coulomb three-body problem in collinear eZe configuration
Classical dynamics of two-electron atom and ions H, He, Li,
Be,... in collinear eZe configuration is investigated. It is revealed
that the mass ratio between necleus and electron plays an important role
for dynamical behaviour of these systems. With the aid of analytical tool and
numeircal computation, it is shown that thanks to large mass ratio ,
classical dynamics of these systems is fully chaotic, probably hyperbolic.
Experimental manifestation of this finding is also proposed.Comment: Largely rewritten. 21 pages. All figures are available in
http://ace.phys.h.kyoto-u.ac.jp/~sano/3-body/index.htm
Kinetic theory of point vortex systems from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy
Kinetic equations are derived from the Bogoliubov-Born-Green-Kirkwood-Yvon
(BBGKY) hierarchy for point vortex systems in an infinite plane. As the level
of approximation for the Landau equation, the collision term of the kinetic
equation derived coincides with that by Chavanis ({\it Phys. Rev. E} {\bf 64},
026309 (2001)). Furthermore, we derive a kinetic equation corresponding to the
Balescu-Lenard equation for plasmas, using the theory of the Fredholm integral
equation. For large , this kinetic equation is reduced to the Landau
equation above.Comment: 10 pages, No figures. To be published in Physical Review E, 76-