Phase Transitions in the Multicomponent Widom-Rowlinson Model and in Hard Cubes on the BCC--Lattice

We use Monte Carlo techniques and analytical methods to study the phase diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M greater or equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M) while for z > z_d(M) there are M demixed phases each consisting mostly of one species. For M=2 there is a direct second order transition from the gas phase to the demixed phase while for M greater or equal 3 the transition at z_d(M) appears to be first order putting it in the Potts model universality class. For M large, Pirogov-Sinai theory gives z_d(M) ~ M-2+2/(3M^2) + ... . In the crystal phase the particles preferentially occupy one of the sublattices, independent of species, i.e. spatial symmetry but not particle symmetry is broken. For M to infinity this transition approaches that of the one component hard cube gas with fugacity y = zM. We find by direct simulations of such a system a transition at y_c ~ 0.71 which is consistent with the simulation z_c(M) for large M. This transition appears to be always of the Ising type.Comment: 11 pages, 4 postscript figures (added in replacement), Physica A (in press

From the adiabatic piston to macroscopic motion induced by fluctuations

The controversial problem of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume one-dimensional ideal fluids separated by a piston whose mass is equal to the mass of the fluid particles we obtain a rigorous explicit stationary non-equilibrium solution of the Boltzmann equation. It is shown that at equal pressures on both sides of the piston, the temperature difference induces a non-zero average velocity, oriented toward the region of higher temperature. It thus turns out that despite the absence of macroscopic forces the asymmetry of fluctuations results in a systematic macroscopic motion. This remarkable effect is analogous to the dynamics of stochastic ratchets, where fluctuations conspire with spatial anisotropy to generate direct motion. However, a different mechanism is involved here. The relevance of the discovered motion to the adiabatic piston problem is discussed.Comment: 14 pages,1 figur

The Collective Coordinates Jacobian

We develop an expansion for the Jacobian of the transformation from particle coordinates to collective coordinates. As a demonstration, we use the lowest order of the expansion in conjunction with a variational principle to obtain the Percus Yevick equation for a monodisperse hard sphere system and the Lebowitz equations for a polydisperse hard sphere system.Comment: 7 page

Gibbs Entropy and Irreversibility

This contribution is dedicated to dilucidating the role of the Gibbs entropy in the discussion of the emergence of irreversibility in the macroscopic world from the microscopic level. By using an extension of the Onsager theory to the phase space we obtain a generalization of the Liouville equation describing the evolution of the distribution vector in the form of a master equation. This formalism leads in a natural way to the breaking of the BBGKY hierarchy. As a particular case we derive the Boltzmann equation

Isolated Gonococcal Extensor Tenosynovitis

Neisseria gonorrhoeae is a mucosal infection that has the propensity to disseminate, causing symptoms that commonly include arthralgias, skin lesions, fevers, chills, dysuria, genital discharge, septic arthritis, and/or tenosynovitis. Typically, gonococcal tenosynovitis affects the flexor sheath and is associated with arthralgias, skin lesions, or both. To the best of our knowledge, there has not been a documented case of isolated gonococcal extensor tenosynovitis. We report the case of a 16-year-old boy with isolated left upper-extremity gonococcal extensor tenosynovitis who was successfully treated with surgical debridement and antibiotic therapy