Abstract
Several years ago, in the course of intense discussions with one of us concerning research problems of mutual interest, our colleague Wolfgang Yourgrau repeatedly employed the colorful term “knots”—perhaps an allusion to the story of Gordius of Phrygia—to denote challenging fundamental dilemmas in the conceptual fabric of physical theory. The galaxy of foundations problems he investigated during his remarkably productive life included, among many other interests, topics in quantal, statistical, and thermal physics. Issues both old and new which arise in efforts to unify these sciences surely qualify as excellent specimens of Professor Yourgrau’s knots in natural philosophy. Hence, to honor his memory, we offer an essay on the knots of quantum thermodynamics. In order to focus mainly upon what Yourgrau used to call “tough science” as opposed to historiographic or metalinguistic analysis, we shall not dwell on the epistemological aspects but proceed immediately to the mathematical foundations of our subject.
… The law that entropy always increases — the second law of thermodynamics — holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations. If it is found to be contradicted by observationwell, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation… .
—Sir Arthur Eddington1
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 and Notes
A. S. Eddington, The Nature of the Physical World (Cambridge U.P., Cambridge, 1928), p. 74.
H. Margenau and J. L. Park, Found. Phys. 3, 19 (1973).
J. L. Park and H. Margenau, Chap. 5 in Perspectives in Quantum Theory ,W. Yourgrau and A. van der Merwe, editors (MIT Press, Cambridge, Massachusetts, 1971).
J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton U.P., Princeton, New Jersey, 1955).
R. Baierlein, Atoms and Information Theory (W. H. Freeman, San Francisco, 1971).
B. K. Skagerstam, Stat. Phys. 12, 449 (1975).
G. N. Hatsopoulos and E. P. Gyftopoulos, Found. Phys. 6, 15 (1976).
G. N. Hatsopoulos and E. P. Gyftopoulos, Found. Phys. 6, 127 (1976).
G. N. Hatsopoulos and E. P. Gyftopoulos, Found. Phys. 6, 439 (1976).
G. N. Hatsopoulos and E. P. Gyftopoulos, Found. Phys. 6, 561 (1976).
M. B. Ruskai, Ann. Inst. Henri Poincaré 19, 357 (1973).
K. Gottfried, Quantum Mechanics Volume I: Fundamentals (W. A. Benjamin, Reading, Massachusetts, 1966), p. 233.
R. Lenk, Brownian Motion and Spin Relaxation (Elsevier, New York, 1977), p. 28.
E. T. Jaynes, Phys. Rev. 106, 620 (1957).
E. T. Jaynes, Phys. Rev. 108, 171 (1957).
E. T. Jaynes, Am. J. Phys. 33, 391 (1965).
A. Katz, Principles of Statistical Mechanics (W. H. Freeman, San Francisco, 1967).
V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).
G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
R. S. Ingarden and A. Kossakowski, Ann. Phys. (N.Y.) 89, 451 (1975).
J. M. Blatt, Prog. Theor. Phys. 22, 745 (1959).
B. Gal-Or, editor, Modern Developments in Thermodynamics (Wiley, New York, 1974).
E. C. Percival, J. Math. Phys. 2, 235 (1961).
R. Jancel, Foundations of Classical and Quantum Statistical Mechanics (Pergamon, New York, 1969).
D. Ruelle, Statistical Mechanics Rigorous Results (W. A. Benjamin, New York, 1969).
I. Prigogine, C. George, F. Henin, and L. Rosenfeld, Chem. Scripta 1973, 4.
I. E. Farquhar, Ergodic Theory in Statistical Mechanics (Interscience, London, 1964).
A. Landé, New Foundations of Quantum Mechanics (University Press, Cambridge, Massachusetts, 1965).
R. Peierls, Surprises in Theoretical Physics (Princeton U.P., Princeton, New Jersey, 1979), p. 73.
A. Landé, New Foundations of Quantum Mechanics (University Press, Cambridge, Massachusetts, 1965), p. 75.
J. Mehra and E. C. G. Sudarshan, Nuovo Cimento 11, 215 (1972).
J. L. Park and W. Band, Found. Phys. 7, 813 (1977).
W. Band and J. L. Park, Found. Phys. 8, 45 (1978).
J. L. Park and W. Band, Found. Phys. 8, 239 (1978).
A. Kossakowski, Bull. Acad. Polon. Sci. Math. 20, 1021 (1972).
A. Kossakowski, Bull. Acad. Polon. Sci. Math. 21, 649 (1973).
A. Kossakowski, Rep. Math. Phys. 3, 247 (1972).
E. B. Davies, Commun. Math. Phys. 39, 91 (1974).
R. F. Simmons and J. L. Park, Found. Phys. 11, 297 (1981).
K. Yosida, Functional Analysis ,4th ed. (Springer-Verlag, New York, 1974), p. 246.
J. L. Park and W. Band, Found. Phys. 1, 211 (1971).
W. Band and J. L. Park, Found. Phys. 1, 339 (1971).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Plenum Press, New York
About this chapter
Cite this chapter
Park, J.L., Simmons, R.F. (1983). The Knots of Quantum Thermodynamics. In: van der Merwe, A. (eds) Old and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8830-2_20
Download citation
DOI: https://doi.org/10.1007/978-1-4684-8830-2_20
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-8832-6
Online ISBN: 978-1-4684-8830-2
eBook Packages: Springer Book Archive