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

Abstract

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 Levy 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 non-exponential 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 Levy and Maxwell distributions.

To appear in Phys. Lett. A

Cited by in corpus (7)

• What should a statistical mechanics satisfy to reflect nature?
• Questioning the validity of non-extensive thermodynamics for classical Hamiltonian systems
• Stable Equilibrium Based on Lévy Statistics: A Linear Boltzmann Equation Approach
• A note on non-thermodynamical applications of non-extensive statistics
• Measuring information growth in fractal phase space
• Truncated Levy distributions in an inelastic gas
• Relativistic Lévy processes