The controversial piston in the thermodynamic limit

We consider the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided in two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where the area $A$ of the container, the number $N$ of particles, and the mass $M$ of the piston go to infinity keeping $\frac{A}M$ and $\frac{N}M$ fixed. We show that in this limit the motion of the piston is deterministic. Introducing simplifying assumptions we discuss the approach to equilibrium and we illustrate the results with numerical simulations. The comparison with the case of a system with finite $(A, N, M)$ will be presented. We consider the evolution of a system composed of $N$ non-interacting point particles of mass $m$ in a container divided in two regions by a movable adiabatic wall (adiabatic piston). In this talk we discuss the thermodynamic limit where the area $A$ of the container, the number $N$ of particles, and the mass $M$ of the piston go to infinity keeping $\frac{A}M$ and $\frac{N}M$ fixed. We show that in this limit the motion of the piston is deterministic. Introducing simplifying assumptions we discuss the approach to equilibrium and we illustrate the results with numerical simulations. The comparison with the case of a system with finite $(A, N, M)$ will be presented.Comment: 7 pages, 3 figures, submitted to Physica

On the adiabatic properties of a stochastic adiabatic wall: Evolution, stationary non-equilibrium, and equilibrium states

The time evolution of the adiabatic piston problem and the consequences of its stochastic motion are investigated. The model is a one dimensional piston of mass $M$ separating two ideal fluids made of point particles with mass $m\ll M$. For infinite systems it is shown that the piston evolves very rapidly toward a stationary nonequilibrium state with non zero average velocity even if the pressures are equal but the temperatures different on both sides of the piston. For finite system it is shown that the evolution takes place in two stages: first the system evolves rather rapidly and adiabatically toward a metastable state where the pressures are equal but the temperatures different; then the evolution proceeds extremely slowly toward the equilibrium state where both the pressures and the temperatures are equal. Numerical simulations of the model are presented. The results of the microscopical approach, the thermodynamical equations and the simulations are shown to be qualitatively in good agreement.Comment: 28 pages, 10 figures include

Multi layer chromosome organization through DNA bending, bridging and extrusion

All living cells have to master the extraordinarily extended and tangly nature of genomic DNA molecules in particular during cell division when sister chromosomes are resolved from one another and confined to opposite halves of a cell. Bacteria have evolved diverse sets of proteins, which collectively ensure the formation of compact and yet highly dynamic nucleoids. Some of these players act locally by changing the path of DNA through the bending of its double helical backbone. Other proteins have wider or even global impact on chromosome organization, for example by interconnecting two distant segments of chromosomal DNA or by actively relocating DNA within a cell. Here, I highlight different modes of chromosome organization in bacteria and on this basis consider models for the function of SMC protein complexes, whose mechanism of action is only poorly understood so far

Choosing a Medicare Part D Plan: Are Medicare Beneficiaries Choosing Low-Cost Plans?

Examines whether Medicare enrollees choose the prescription drug plans with the lowest premiums and out-of-pocket expenses for them from among multiple private insurance options. Estimates how much enrollees would have saved with the lowest-cost plan