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4
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17044421499
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G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995); J. Stat. Phys. 80, 931 (1995).
-
(1995)
J. Stat. Phys.
, vol.80
, pp. 931
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-
-
8
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-
33645095806
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-
note
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The dynamical systems are required to have an isoenergetic Gaussian thermostat for this to be strictly true, otherwise correction terms appear, though these might possibly vanish in the large time or system size limit.
-
-
-
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10
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-
33645084095
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-
note
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Also, the integrated TFT and SSFT exist [11,12], which we do not discuss here since they are constructed only to improve the statistics in experiments or simulations.
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-
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15
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33645073755
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O. Mazonka and C. Jarzynski, e-print cond-mat/9912121
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O. Mazonka and C. Jarzynski, e-print cond-mat/9912121.
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-
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16
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33645094757
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note
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In Eq. (12) the possibility of energy being stored as kinetic energy of the Brownian particle has been neglected. While this in principle should be included, fluctuations in velocity decay on a time scale ≪ 1 in the overdamped case, so that we may neglect them on time scales of O(1).
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-
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17
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0004161838
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Cambridge University Press, Cambridge
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, 1992).
-
(1992)
Numerical Recipes in Fortran, the Art of Scientific Computing, 2nd Ed.
-
-
Press, W.H.1
Teukolsky, S.A.2
Vetterling, W.T.3
Flannery, B.P.4
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18
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0003598496
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Cambrige University Press, Cambridge
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H. Jeffreys and B. S. Jeffreys, Methods of Mathematical Physics, 3rd ed. (Cambrige University Press, Cambridge, 1956); P. Dennery and A. Krzywicki, Mathematics for Physicists (Harper and Row, New York, 1967). L. Sirovich, Techniques of Asymptotic Analysis (Springer-Verlag, New York, 1971).
-
(1956)
Methods of Mathematical Physics, 3rd Ed.
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-
Jeffreys, H.1
Jeffreys, B.S.2
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19
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-
0004294506
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Harper and Row, New York
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H. Jeffreys and B. S. Jeffreys, Methods of Mathematical Physics, 3rd ed. (Cambrige University Press, Cambridge, 1956); P. Dennery and A. Krzywicki, Mathematics for Physicists (Harper and Row, New York, 1967). L. Sirovich, Techniques of Asymptotic Analysis (Springer-Verlag, New York, 1971).
-
(1967)
Mathematics for Physicists
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-
Dennery, P.1
Krzywicki, A.2
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20
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-
0003980022
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-
Springer-Verlag, New York
-
H. Jeffreys and B. S. Jeffreys, Methods of Mathematical Physics, 3rd ed. (Cambrige University Press, Cambridge, 1956); P. Dennery and A. Krzywicki, Mathematics for Physicists (Harper and Row, New York, 1967). L. Sirovich, Techniques of Asymptotic Analysis (Springer-Verlag, New York, 1971).
-
(1971)
Techniques of Asymptotic Analysis
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-
Sirovich, L.1
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21
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33645083557
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-
note
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Q in Eq. (38) if ≳3.
-
-
-
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22
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-
33645074768
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-
note
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2] for large q, so that on the rhs of Eq. (38) the integral for the Fourier inverse diverges for τ< 2. This is an artifact of neglecting the exponentials.
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-
-
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23
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-
0004149831
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-
Cambridge University Press, Cambridge
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S. Wolfram, The Mathematica Book (Cambridge University Press, Cambridge, 1999).
-
(1999)
The Mathematica Book
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-
Wolfram, S.1
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24
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-
33645048814
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-
note
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It is useful to have an analytic result for the saddle points in MATHEMATICA's memory because this shows that q* is a smooth function of p and allows for the derivative ∂q*/∂p needed in Eq. (53) to be obtained as well.
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-
-
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25
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-
33645051796
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-
note
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-2α-β), respectively, so that h(q*)=h(x) + O(τ-α-min(α,β)).
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-
-
-
26
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-
33645090265
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-
note
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-1) correction in Eq. (61).
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-
-
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27
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-
33645053862
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-
note
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d-2/64 and -d/2, resp. Finally, in Eq. (69) 1/w becomes d/(3w).
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-
-
-
30
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33645080756
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-
L. Rey-Bellet, e-print math-ph/0303021
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L. Rey-Bellet and L. E. Thomas, Ann. Henri Poincare 3, 483 (2002); L. Rey-Bellet, e-print math-ph/0303021.
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