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

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

The Wealth of the Unemployed: Adequacy and Implications for Unemployment Insurance

While there has been considerable discussion of the adequacy of unemployment insurance (UI) benefits as a form of income replacement, there is little evidence on the other resources that the unemployed have to finance their unemployment spells. In this paper I focus on focus on one form of resources, own wealth holdings. I find that the median worker has financial assets sufficient to finance roughly two-thirds of the income loss from an unemployment spell, but that there is tremendous heterogeneity in wealth holdings; almost one-third of workers can't even replace 10% of their income loss. Most strikingly, ex-ante wealth holdings decline precipitously with realized unemployment durations, both absolutely and (especially) relative to ex-post income loss, suggesting that adequacy could be increased if UI benefits were targeted to those with longer spells. I also find strong evidence that individuals who are eligible for more generous UI draw down their wealth more slowly during unemployment spells. This demonstrates that wealth is used as a consumption smoothing device alongside UI to cope with the income loss from unemployment.