Thermal measurements of stationary nonequilibrium systems: A test for generalized thermostatistics

We show that a gas thermometer in contact with a stationary classical system out of thermal (Boltzmann) equilibrium evolves, under very general conditions, towards a state characterized by a Lévy velocity distribution. Our approach is based on a kinetic-like equation that applies to a wide class of models for the system-thermometer interaction. The results clarify the role of nonexponential energy distributions as possible generalizations of the Boltzmann distribution for systems where the usual formulation of thermostatistics may not apply. In particular, they show that the power-law distributions derived from Tsallis's nonextensive formalism are irrelevant to the stationary state of the thermometer, thus failing to give a consistent description of the system-thermometer equilibrium. We point out the need of a generalized thermostatistical formulation able to give a unified frame to Lévy and Maxwell distributions. © 2003 Elsevier B.V. All rights reserved.