Abstract
We study networks of interacting oscillators, driven at the boundary by heat baths at possibly different temperatures. A set of first elementary questions are discussed concerning the uniqueness of a stationary possibly Gibbsian density and the nature of the entropy production and the local heat currents. We also derive a Carnot efficiency relation for the work that can be extracted from the heat engine.
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J.-P. Eckmann, C.-A. Pillet, and L. Rey-Bellet, Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures, Commun. Math. Phys. 201:657(1999).
J.-P. Eckmann, C.-A. Pillet, and L. Rey-Bellet, Entropy production in nonlinear, thermally driven Hamiltonian systems, J. Stat. Phys. 95:305(1999).
G. W. Ford, M. Kac, and P. Mazur, Statistical mechanics of assemblies of coupled oscillators, J. Math. Phys. 6:504-515 (1965).
J. Fritz, Stationary states of hamiltonian systems with noise, in On Three Levels, M. Fannes, C. Maes, and A. Verbeure, eds. (Plenum Press, New York, 1994), pp. 203-214.
J. Fritz, T. Funaki, and J. L. Lebowitz, Stationary states of random hamiltonian systems, Probab. Theory Related Fields 99:211-236 (1994).
J. L. Lebowitz, Stationary nonequilibrium Gibbsian ensemble, Phys. Rev. 114:1192-1202 (1959).
R. S. Lipster and A. N. Shiryayev, Statistics of Random Processes I, II (Springer-Verlag, New York/Heidelberg/Berlin, 1978).
C. Maes, Fluctuation theorem as a Gibbs property, J. Stat. Phys. 95:367-392 (1999).
C. Maes and K. Netočn ý, Time-reversal and entropy, J. Stat. Phys. 110:269-310 (2003).
H. Nakazawa, On the lattice thermal conduction, Suppl. Prog. Theor. Phys. 45:231-262 (1970).
L. Rey-Bellet and L. E. Thomas, Fluctuations of the entropy production in anharmonic chains, Ann. Henri Poincaré 3:483-502 (2002).
L. Rey-Bellet and L. E. Thomas, Asymptotic behavior of thermal nonequilibrium steady states for a driven chain of anharmonic oscillators, Commun. Math. Phys. 215:1-24 (2000).
Z. Rieder, J. L. Lebowitz, and E. Lieb, Properties of a harmonic crystal in a stationary nonequilibrium state, J. Math. Phys. 8:1073-1078 (1967).
H. Spohn and J. L. Lebowitz, Stationary non-equilibrium states of infinite harmonic systems, Commun. Math. Phys. 54:97-120 (1977).
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Maes, C., Netočný, K. & Verschuere, M. Heat Conduction Networks. Journal of Statistical Physics 111, 1219–1244 (2003). https://doi.org/10.1023/A:1023004300229
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DOI: https://doi.org/10.1023/A:1023004300229