Fluctuations and response of nonequilibrium states

A generalized fluctuation-response relation is found for thermal systems driven out of equilibrium. Its derivation is independent of many details of the dynamics, which is only required to be first-order. The result gives a correction to the equilibrium fluctuation-dissipation theorem, in terms of the correlation between observable and excess in dynamical activity caused by the perturbation. Previous approaches to this problem are recovered and extended in a unifying scheme

Response theory: a trajectory-based approach

We collect recent results on deriving useful response relations also for nonequilibrium systems. The approach is based on dynamical ensembles, determined by an action on trajectory space. (Anti)Symmetry under time-reversal separates two complementary contributions in the response, one entropic the other frenetic. Under time-reversal invariance of the unperturbed reference process, only the entropic term is present in the response, giving the standard fluctuation-dissipation relations in equilibrium. For nonequilibrium reference ensembles, the frenetic term contributes essentially and is responsible for new phenomena. We discuss modifications in the Sutherland-Einstein relation, the occurence of negative differential mobilities and the saturation of response. We also indicate how the Einstein relation between noise and friction gets violated for probes coupled to a nonequilibrium environment. We end with some discussion on the situation for quantum phenomena, but the bulk of the text concerns classical mesoscopic (open) systems. The choice of many simple examples is trying to make the notes pedagogical, to introduce an important area of research in nonequilibrium statistical mechanics

The celestial city brought down to earth : Dmitrij Cernákov's interpretation of Rimskij-Korsakov's opera the invisible city of Kitež and the Maiden Fevronia

Rimsky-Korsakov's penultimate opera is tied to the symbolist movement in fin de siècle Russia. Although the composer did not intend it as a mystical work in the wake of Wagner's Parsifal, his symbolist collaborators invested much symbolist thinking in the production. In contemporary reception, however, the eschatological focus of the work is hard to adjust to the expectations of modern audiences. This paper discusses the solutions elaborated by the Russian stage director Dimitry Tcherniakov in his production for the National Opera in Amsterdam. Tcherniakov succeeded to manipulate the work into the direction of a social and psychological drama. This paper analyses the strategies he employed to arrive at such a significant change of meaning without violating its spiritual tone

The Fluctuation Theorem as a Gibbs Property

Common ground to recent studies exploiting relations between dynamical systems and non-equilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity principle) underlying the Gallavotti-Cohen fluctuation theorem make it possible, using symbolic dynamics, to employ the theory of one-dimensional lattice spin systems. The Kurchan and Lebowitz-Spohn analysis of this fluctuation theorem for stochastic dynamics can be restated on the level of the space-time measure which is a Gibbs measure for an interaction determined by the transition probabilities. In this note we understand the fluctuation theorem as a Gibbs property as it follows from the very definition of Gibbs state. We give a local version of the fluctuation theorem in the Gibbsian context and we derive from this a version also for some class of spatially extended stochastic dynamics

The End Of Art Revisited: A Response To Kalle Puolakka

In ‘The End of Art: A Real Problem or Not Really a Problem?’ I raised some questions about Arthur Danto’s famous ‘end of art’ thesis. A largely polemical paper, it was intended as an invitation to further discussion, and Kalle Puolakka has now taken up this invitation in ‘Playing The Game After The End of Art’. I thank him for his many insightful remarks. Critical comments are typically more interesting and helpful than simple praise, and Puolakka’s comments are no exception. I would therefore like to return the favour. I will place Puolakka’s remarks under critical examination and in the process hope to rephrase, refine, and defend some of my original claims. First, however, I will briefly restate my reading of Danto’s ideas on the end of art