Scaling functions for nonequilibrium fluctuations: A picture gallery

The emergence of non-gaussian distributions for macroscopic quantities in nonequilibrium steady states is discussed with emphasis on the effective criticality and on the ensuing universality of distribution functions. The following problems are treated in more detail: nonequilibrium interface fluctuations (the problem of upper critical dimension of the Kardar-Parisi-Zhang equation), roughness of signals displaying Gaussian 1/f power spectra (the relationship to extreme-value statistics), effects of boundary conditions (randomness of the digits of pi).Comment: Invited contribution at SPIE conference on Fluctuations and Noise, Santa Fe, 2003; 9 pages, 6 figure

Does the third law of black hole thermodynamics really have a serious failure?

The almost perfect correspondence between certain laws of classical black hole mechanics and the ordinary laws of thermodynamics is spoiled by the failure of the conventional back hole analogue of the third law. Our aim here is to contribute to the associated discussion by flashing light on some simple facts of black hole physics. However, no attempt is made to lay to rest the corresponding long lasting debate. Instead, merely some evidence is provided to make it clear that although the borderline between extremal and non-extremal black holes is very thin they are essentially different. Hopefully, a careful investigation of the related issues will end up with an appropriate form of the third law and hence with an unblemished setting of black hole thermodynamics.Comment: 6 pages, Latex. accepted for publication in Class. Quant. Gra

Large deviations in weakly interacting boundary driven lattice gases

One-dimensional, boundary-driven lattice gases with local interactions are studied in the weakly interacting limit. The density profiles and the correlation functions are calculated to first order in the interaction strength for zero-range and short-range processes differing only in the specifics of the detailed-balance dynamics. Furthermore, the effective free-energy (large-deviation function) and the integrated current distribution are also found to this order. From the former, we find that the boundary drive generates long-range correlations only for the short-range dynamics while the latter provides support to an additivity principle recently proposed by Bodineau and Derrida.Comment: 27 pages, 2 figure