Entropy Production in the Theory of Heat Conduction in Solids

• Main Author: Federico Zullo
• Format: Article
• Language: English
• Published: MDPI AG 2016-03-01
• Series: Entropy
• Subjects: non-equilibrium thermodynamics; entropy; heat transfer; minimum entropy production
• Online Access: http://www.mdpi.com/1099-4300/18/3/87

The evolution of the entropy production in solids due to heat transfer is usually associated with the Prigogine’s minimum entropy production principle. In this paper, we propose a critical review of the results of Prigogine and some comments on the succeeding literature. We suggest a characterization of the evolution of the entropy production of the system through the generalized Fourier modes, showing that they are the only states with a time independent entropy production. The variational approach and a Lyapunov functional of the temperature, monotonically decreasing with time, are discussed. We describe the analytic properties of the entropy production as a function of time in terms of the generalized Fourier coefficients of the system. Analytical tools are used throughout the paper and numerical examples will support the statements.