Abstract
We obtain a general quantum statistical derivation of thermodynamics with phase structure on the basis of the model in which many-particle systems are idealized as infinite. Macroscopic observables, corresponding to global densities of extensive conserved quantities, are explicitly introduced into the model to serve as thermodynamic variables. The resultant thermodynamics, expressed in terms of these variables and their conjugates, supports a phase structure characterized both by singularities in the Gibbs potential and by coexistent, macroscopically distinct, equilibrium states. It is noteworthy that, by contrast, the traditional statistical mechanics of finite systems could not support either of these characterizations of thermodynamic phase structure.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
O. Bratteli and D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Springer, Heidelberg/New York, Vol. 1, 1979; Vol. 2, 1981.
H. Callen, Thermodynamics, Wiley, New York, 1960.
D.A. Dubin, Solvable Models in Algebraic Statistical Mechanics, Clarendon Press, Oxford, 1974.
G. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley, New York/London, 1972.
H. Fröhlich, in Proc. 1st Int. Conf. Theor. Phys. Biol., H. Maurois, Ed., North Holland, Amsterdam, 1969, pp. 13–22.
H. Fröhlich, Nuovo Cimento 3, 490 (1973).
L.D. Landau and E.M. Lifshitz, Statistical Physics, Pergamon, London/New York, 1959.
O.E. Lanford and D.W. Robinson, Commun. Math. Phys. 9, 327 (1968a).
O.E. Lanford and D.W. Robinson, J. Math. Phys. 9, 1120 (1968b).
J.L. Lebowitz, Ann. Rev. Phys. Chem. 19, 389 (1968).
J.L. Lebowitz, J. Stat. Phys. 16, 463 (1977).
A. Messager and S. Miracle-Sole, Commun. Math. Phys.40, 187 (1975).
L. Onsager, Phys. Rev. 65, 117 (1944).
A.W. Roberts and D.E. Varberg, Convex Functions, Academic, London/New York, 1973.
D.W. Robinson, The Thermodynamical Pressure in Quantum Statistical Mechanics, Lecture Notes in Physics, Vol. 9, Springer, Berlin/Heidelberg/New York, 1971.
D. Ruelle, Statistical Mechanics, W.A. Benjamin, New York, 1969.
G.L. Sewell, Quantum Theory of Collective Phenomena, Clarendon Press, Oxford, 1986 (to appear).
W. Thirring, Quantum Theory of Large Systems, Springer, New York/Vienna, 1980.
L. Tisza, (and others), Generalized Thermodynamics, M.I.T. Press, Cambridge, MA, and London, 1966.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sewell, G.L. (1987). Quantum Statistical Basis of Thermodynamics with Phase Structure. In: Barrett, T.W., Pohl, H.A. (eds) Energy Transfer Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71867-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-71867-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17502-5
Online ISBN: 978-3-642-71867-0
eBook Packages: Springer Book Archive