Blast Dynamics in a Dissipative Gas.

The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution is a prototypical example of self-similarity driven by conservation laws. In dissipative media, however, energy conservation is violated, yet a distinctive self-similar solution appears. It hinges on the decoupling of random and coherent motion permitted by a broad class of dissipative mechanisms. This enforces a peculiar layered structure in the shock, for which we derive the full hydrodynamic solution, validated by a microscopic approach based on molecular dynamics simulations. We predict and evidence a succession of temporal regimes, as well as a long-time corrugation instability, also self-similar, which disrupts the blast boundary. These generic results may apply from astrophysical systems to granular gases, and invite further cross-fertilization between microscopic and hydrodynamic approaches of shock waves.

Fluctuations in partitioning systems with few degrees of freedom.

We study the behavior of a moving wall in contact with a particle gas and subjected to an external force. We compare the fluctuations of the system observed in the microcanonical and canonical ensembles, by varying the number of particles. Static and dynamic correlations signal significant differences between the two ensembles. Furthermore, velocity-velocity correlations of the moving wall present a complex two-time relaxation that cannot be reproduced by a standard Langevin-like description. Quite remarkably, increasing the number of gas particles in an elongated geometry, we find a typical time scale, related to the interaction between the partitioning wall and the particles, which grows macroscopically.

Nonequilibrium and information: the role of cross correlations.

We discuss the relevance of information contained in cross correlations among different degrees of freedom, which is crucial in nonequilibrium systems. In particular we consider a stochastic system where two degrees of freedom X{1} and X{2}-in contact with two different thermostats-are coupled together. The production of entropy and the violation of equilibrium fluctuation-dissipation theorem (FDT) are both related to the cross correlation between X{1} and X{2}. Information about such cross correlation may be lost when single-variable reduced models for X_{1} are considered. Two different procedures are typically applied: (a) one totally ignores the coupling with X{2}; and (b) one models the effect of X{2} as an average memory effect, obtaining a generalized Langevin equation. In case (a) discrepancies between the system and the model appear both in entropy production and linear response; the latter can be exploited to define effective temperatures, but those are meaningful only when time scales are well separated. In case (b) linear response of the model well reproduces that of the system; however the loss of information is reflected in a loss of entropy production. When only linear forces are present, such a reduction is dramatic and makes the average entropy production vanish, posing problems in interpreting FDT violations.