Nonequilibrium stationary states and entropy

G. Gallavotti; E. G. D. Cohen

doi:10.1103/PhysRevE.69.035104

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Nonequilibrium stationary states and entropy

G. Gallavotti^1,* and E. G. D. Cohen^2,†

¹Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854, USA
²Rockefeller University, New York, New York 10021, USA

^*Permanent address: Dipartimento di Fisica and INFN, Universitá Roma 1, Piazzale Aldo Moro, 00185 Roma, Italy. Email address: gallavotti@roma1.infn.it
^†Email address: egdc@mail.rockefeller.edu

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Phys. Rev. E 69, 035104(R) – Published 31 March, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.035104

Abstract

In transformations between nonequilibrium stationary states, entropy might not be a well defined concept. It might be analogous to the “heat content” in transformations in equilibrium which is not well defined either, if they are not isochoric (i.e., do involve mechanical work). Hence we conjecture that in a nonequilibrium stationary state the entropy is just a quantity that can be transferred or created, such as heat in equilibrium, but has no physical meaning as “entropy content” as a property of the system.

References (29)

M. W. Zemansky, Heat and Thermodynamics (McGraw-Hill, New York, 1957).
G. Gallavotti, in Meteorological and Geophysical Fluid Dynamics, edited by W. Schröder (Science, Bremen, 2004).
G. Gallavotti, Foundations of Fluid Dynamics (Springer-Verlag, Berlin, 2002).
G. Gallavotti and E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995).
S. de Groot and P. Mazur, Non Equilibrium Thermodynamics (Dover, Mineola, NY, 1984).
K. Feitosa and N. Menon, e-print cond-mat/0308212.
R. Becker, Electromagnetic Fields and Interactions (Blaisdell, New-York, 1964).
D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Fluids (Academic, New York, 1990).
G. Gallavotti, Phys. Rev. Lett. 77, 4334 (1996).
D. Ruelle, Turbulence, Strange Attractors and Chaos (World Scientific, New York, 1995).
G. Gallavotti, Statistical Mechanics: A Short Treatise (Springer-Verlag, Berlin, 2000).
G. Gallavotti, F. Bonetto, and G. Gentile, Aspects of the Ergodic, Qualitative and Statistical Theory of Motion (Springer-Verlag, Berlin, 2004).
L. Boltzmann. Über die Eigenshaften Monozyklischer und Anderer Damit Verwandter Systeme, Wissenschafltliche Abhandlungen, Vol. 3 (Chelsea, New-York, 1968).
L. D. Landau and E. M. Lifschitz Statistical Physics (Pergamon Press, London, 1958).
L. Andrej, Phys. Lett. 111A, 45 (1982).
D. Ruelle, J. Stat. Phys. 95, 393 (1999).
D. Ruelle, J. Stat. Phys. 85, 1 (1996).
L.F. Cugliandolo, J. Kurchan, and L. Peliti, Phys. Rev. E 55, 3898 (1997).
G. Gallavotti, J. Stat. Phys. 84, 899 (1996).
G. Gallavotti and D. Ruelle, Commun. Math. Phys. 190, 279 (1997).
D. Evans and L. Rondoni, J. Stat. Phys. 109, 895 (2002).
J. Lebowitz, Phys. Today 46, 32 (1993).
D. Ruelle, Proc. Natl. Acad. Sci. U.S.A. 100, 3054 (2003).
P. Garrido, S. Goldstein, and J. Lebowitz, e-print cond-math/0310575.
D.J. Evans, E.G.D. Cohen, and G. Morriss, Phys. Rev. Lett. 71, 2401 (1993).
F. Bonetto, G. Gallavotti, and P. Garrido, Physica D 105, 226 (1997).
G. Gentile, Forum Math. 10, 89 (1998).
G. Gallavotti, L. Rondoni, and E. Segre, Physica D 187, 358 (2004).
S. Ciliberto, N. Garnier, S. Hernandez, C. Lacpatia, J.F. Pinton, and G. Ruiz Chavarria, e-print nlin.cd/0311037.

[c1] M. W. Zemansky, Heat and Thermodynamics (McGraw-Hill, New York, 1957).

[c2] G. Gallavotti, in Meteorological and Geophysical Fluid Dynamics, edited by W. Schröder (Science, Bremen, 2004).

[c3] G. Gallavotti, Foundations of Fluid Dynamics (Springer-Verlag, Berlin, 2002).

[c4] G. Gallavotti and E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995).

[c5] S. de Groot and P. Mazur, Non Equilibrium Thermodynamics (Dover, Mineola, NY, 1984).

[c6] K. Feitosa and N. Menon, e-print cond-mat/0308212.

[c7] R. Becker, Electromagnetic Fields and Interactions (Blaisdell, New-York, 1964).

[c8] D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Fluids (Academic, New York, 1990).

[c9] G. Gallavotti, Phys. Rev. Lett. 77, 4334 (1996).

[c10] D. Ruelle, Turbulence, Strange Attractors and Chaos (World Scientific, New York, 1995).

[c11] G. Gallavotti, Statistical Mechanics: A Short Treatise (Springer-Verlag, Berlin, 2000).

[c12] G. Gallavotti, F. Bonetto, and G. Gentile, Aspects of the Ergodic, Qualitative and Statistical Theory of Motion (Springer-Verlag, Berlin, 2004).

[c13] L. Boltzmann. Über die Eigenshaften Monozyklischer und Anderer Damit Verwandter Systeme, Wissenschafltliche Abhandlungen, Vol. 3 (Chelsea, New-York, 1968).

[c14] L. D. Landau and E. M. Lifschitz Statistical Physics (Pergamon Press, London, 1958).

[c15] L. Andrej, Phys. Lett. 111A, 45 (1982).

[c16] D. Ruelle, J. Stat. Phys. 95, 393 (1999).

[c17] D. Ruelle, J. Stat. Phys. 85, 1 (1996).

[c18] L.F. Cugliandolo, J. Kurchan, and L. Peliti, Phys. Rev. E 55, 3898 (1997).

[c19] G. Gallavotti, J. Stat. Phys. 84, 899 (1996).

[c20] G. Gallavotti and D. Ruelle, Commun. Math. Phys. 190, 279 (1997).

[c21] D. Evans and L. Rondoni, J. Stat. Phys. 109, 895 (2002).

[c22] J. Lebowitz, Phys. Today 46, 32 (1993).

[c23] D. Ruelle, Proc. Natl. Acad. Sci. U.S.A. 100, 3054 (2003).

[c24] P. Garrido, S. Goldstein, and J. Lebowitz, e-print cond-math/0310575.

[c25] D.J. Evans, E.G.D. Cohen, and G. Morriss, Phys. Rev. Lett. 71, 2401 (1993).

[c26] F. Bonetto, G. Gallavotti, and P. Garrido, Physica D 105, 226 (1997).

[c27] G. Gentile, Forum Math. 10, 89 (1998).

[c28] G. Gallavotti, L. Rondoni, and E. Segre, Physica D 187, 358 (2004).

[c29] S. Ciliberto, N. Garnier, S. Hernandez, C. Lacpatia, J.F. Pinton, and G. Ruiz Chavarria, e-print nlin.cd/0311037.

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