Temperature gradients in equilibrium: small microcanonical systems in an external field
arXiv:1409.6737 · doi:10.1103/PhysRevE.90.052127
Abstract
We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble the system i) obeys a barometric formula for the density profile and ii) the kinetic temperature is independent of height, even when the system is small. We show here that in the microcanonical ensemble the kinetic temperature of the particles affected by the field is not constant with height, but that rather, generally speaking, it decreases with a gradient of order 1/N. Even more, if we have a mixture of two species, one which is influenced by the field and the other which is not, we find that the two species' kinetic temperatures are generally different, even at the same height. These facts are shown in detail by studying a simple mechanical model: a Lorentz Gas where particles and spinning disks interact and the particles are subjected to a constant external force. In the microcanonical ensemble, the kinetic temperature of the particles is indeed found to vary with height; the disks' kinetic temperature, on the other hand, is height-independent, and thus, differs from that of the particles with which they interact.
arXiv comment16 pp, 3 figures
References in corpus (6)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Negative Specific Heat in Astronomy, Physics and Chemistry
- Negative heat capacity in the critical region of nuclear fragmentation: an experimental evidence of the liquid-gas phase transition
- Observation of coupled normal heat and matter transport in a simple model system
- Violation of the Zeroth Law of Thermodynamics in Systems with Negative Specific Heat
- Transport properties of a modified Lorentz gas