  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.
