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Entropy 2016, 18(3), 87; doi:10.3390/e18030087

Entropy Production in the Theory of Heat Conduction in Solids

1
Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, 00146 Roma, Italy
2
INFN Section of Roma Tre, Department of Mathematics and Physics, Via della Vasca Navale 84, 00146 Roma, Italy
Academic Editors: Umberto Lucia, Giuseppe Grazzini and Kevin H. Knuth
Received: 11 January 2016 / Revised: 13 February 2016 / Accepted: 26 February 2016 / Published: 8 March 2016
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Abstract

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. View Full-Text
Keywords: non-equilibrium thermodynamics; entropy; heat transfer; minimum entropy production non-equilibrium thermodynamics; entropy; heat transfer; minimum entropy production
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Zullo, F. Entropy Production in the Theory of Heat Conduction in Solids. Entropy 2016, 18, 87.

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