Corrigenda

• P. 204, first paragraph of Example 4.27: "its attractive nature and its tendency to reduce fluctuations" should read "its attractive nature and its tendency to reduce fluctuations at short distances"
• The step (5.63) in the proposed simulation algorithm for bead-rod-spring models with hydrodynamic interactions is incorrect, and it is actually at variance with the correct mnemonic remarks at the end of Section 5.1.4. According to those mnemonic remarks, the unconstrained move (5.63) should contain the divergence of the hydrodynamic interaction tensors as given in (4.64); however, this divergence-term is missing in (5.63). The omission of this verbally postulated contribution in the corresponding equation is a consequence of a sloppiness in calculating the space derivative \({\scriptsize (\partial/\partial \mathbf{r}_{\nu'})(\partial \mathbf{R}_\nu/\partial g_j)}\) in the last line of (5.65); as a consequence, (5.65), which is consistent with the incorrectly formulated move (5.63) based on it, actually differs from (5.61) by a term which corresponds exactly to the missing divergence-term in (5.63). [I'm grateful to David C. Morse for pointing out this error; for a detailed discussion, see David C. Morse, Theory of Constrained Brownian Motion, Advances in Chemical Physics 128 (2004) 65-189.]
• A factor of 2 is missing in (6.13) [the factor 6 should be replaced by 12]
• Typo: The o in "of" should be underlined in the last line of p. 13
• Typo: "Interweaved" should read "interwoven" on back cover

Additions

3.3.4 Mean Field Interactions

One can ask the question whether the nonlinear diffusion equations for processes with mean field interactions describe Markov processes. Actually, a full stochastic process must first be associated with a nonlinear diffusion equation for the single-time probability density, which can be done naturally through the corresponding stochastic differential equation. It was discussed by T.D. Frank [Physica A 320 (2003) 204-210] that, in general, the resulting process does not satisfy the Markov property.

4.2.4 Gaussian Approximation

The significance of the violation of the Green-Kubo formula for the viscosity within the Gaussian approximation (see p. 202) has been further discussed by M. Hütter and H.C. Öttinger [Phys. Rev. E54 (1996) 2526-2530] and by M. Hütter, I.V. Karlin and H.C. Öttinger [Phys. Rev. E68 (2003) 016115].

The problems occurring in the formulation of a Gaussian approximation for the transition probabilities (as discussed on p. 202) may be related to the non-Markovian character of processes with mean field interactions (see addition to Section 3.3.4).