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Entropy 2017, 19(7), 350; https://doi.org/10.3390/e19070350

Fourier’s Law in a Generalized Piston Model

1
GSSI (Gran Sasso Science Institute), Università dell’Aquila, Viale Francesco Crispi, 7, 67100 L’Aquila, Italy
2
Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
3
ISC-CNR and Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
4
Centro Interdisciplinare B. Segre, Accademia dei Lincei, Via della Lungara, 10, 00165 Rome, Italy
*
Author to whom correspondence should be addressed.
Received: 5 June 2017 / Revised: 3 July 2017 / Accepted: 6 July 2017 / Published: 11 July 2017
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Abstract

A simplified, but non trivial, mechanical model—gas of N particles of mass m in a box partitioned by n mobile adiabatic walls of mass M—interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantities for the stationary non-equilibrium states. The results are compared with extensive numerical simulations; in the limit of large n, m N / M 1 and m / M 1 , we find a good approximation of Fourier’s law. View Full-Text
Keywords: Fourier’s law; kinetic theory; non equilibrium statistical mechanics Fourier’s law; kinetic theory; non equilibrium statistical mechanics
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Caprini, L.; Cerino, L.; Sarracino, A.; Vulpiani, A. Fourier’s Law in a Generalized Piston Model. Entropy 2017, 19, 350.

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