Equilibrium temperature anisotropy and black-hole analogues

When long-range interactions are present the usual definition of temperature implies that two systems in thermal equilibrium can be at different temperatures. This local temperature has physical significance, if the sub-systems cease to interact, each system will be at their different local temperatures. This is formally related to redshifting of temperature in general relativity. We propose experiments to test this effect which are feasible using current microfabrication techniques. It is also possible to display thermodynamical analogues to black-hole space-time.