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

Legal entity in electronic commerce

Abstract of the German original article “Rechtssubjekte und Teilrechtssubjekte des elektronischen Geschäftsverkehrs“, to be published in S. Beck (ed.): Jenseits von Mensch und Maschine: Moralische und rechtliche Aspekte des Umgangs mit Robotern, Künstlicher Intelligenz und Cyborgs. Baden-Baden: Nomos, 2012