On the speed of heat waves

BME Instutute of Nuclear Techniques - Budapest, H-1111 Müegyetem rkp. 3, R-317, Hungary, EU and KFKI Atomic Energy Research Institute - H-1525 Budapest 114, POB 49, Hungary, EU

^a makai@reak.bme.hu

Received: 18 May 2011
Accepted: 30 September 2011

Abstract

We revisit the problem of heat conductance and diffusion, two remarkable transport processes characterized by instantaneous actions. We show that the assumption of local thermal equilibrium sets a limit to the speed of change in the distribution function of a statistical system . A statistical system consists of a large number of components, and its state is changed through a large number if interactions among its components. A macroscopic phenomenon is obtained by averaging, thus it would be rather unexpected if any macroscopic phenomenon would exhibit a speed faster than the change rate of the distribution function itself. Using Onsager's approximation, we show that the balance equations of the extensive parameters also have solutions with finite velocities involved. At the same time the infinite speed is obtainable when second-order terms are neglected. We show how the presented technique is applied in plasma physics to determine the speeds of transport processes in fusion plasmas.