Abstract
The use of joint distribution functions for noncommuting observables in quantum thermodynamics is investigated in the light of L. Cohen's proof that such distributions are not determined by the quantum state. Cohen's proof is irrelevant to uses of the functions that do not depend on interpreting them as distributions. An example of this, from quantum Onsager theory, is discussed. Other uses presuppose that correlations betweenp andq values depend at least on the state. But correlations may be fixed by the state even though the distribution varies from one ensemble to another represented by that state. Taking covariance as a measure of correlation, it is shown that the different commonly used joint distributions yield the same correlations for a given state. A general characterization is given for a family of distributions with this same covariance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Cohen, Thesis. Yale University 1966, University Microfilm, Ann Arbor, Michigan; H. Margenau and L. Cohen, inQuantum Theory and Reality, M. Bunge, ed. (Springer-Verlag, New York, 1967).
E. Wigner,Phys. Rev. 40, 749 (1932).
E. Wigner, inPerspectives in Quantum Theory: Essays in Honor of Alfred Lande, M. Yourgrau and van der Merwe, eds. (MIT Press, Cambridge, Massachusetts, 1971).
M. Gardner,Brit. J. Phil. Sci. 23, 13 (1972).
A. Fine,Brit. J. Phil. Sci. 24, 1 (1973).
J. Park and H. Margenau, inPerspectives in Quantum Theory: Essays in Honor of Alfred Lande, W. Yourgrau and A. van der Merwe, eds. (MIT Press, Cambridge, Massachusetts 1971).
B. van Fraassen, inContemporary Research in the Philosophy and Foundation Quantum Mechanics, C. A. Hooker, ed. (Reidel, 1973).
J. Vlieger, P. Mazur, and S. R. DeGroot, Statistical Basis of Non-Equilibrium Thermodynamics, I, II, and III,Physica 27, 353, 957, and 974 (1961).
H. S. Groenewold,Physica 12, 405 (1946).
H. Mori, I. Oppenheim, and J. Ross, inStudies in Statistical Mechanics, Vol. I, J. DeBoer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1962).
S. Ono, inProc. of the International Symposium on Transport Processes in Statistical Mechanics, Brussels 1956, I. Prigogine, ed. (Interscience, New York, 1958).
H. Mori and S. Ono,Progr. Theor. Phys. 8, 327 (1952).
H. Weyl,Z. Phys. 46, 1 (1927).
J. von Neumann,Mathematical Foundations of Quantum Mechanics, transl. by R. T. Beyer (Princeton University Press, Princeton, New Jersey, 1955).
Author information
Authors and Affiliations
Additional information
Part of this research was sponsored by a National Science Foundation Post-doctoral Fellowship.
Rights and permissions
About this article
Cite this article
Cartwright, N. Correlations without joint distributions in quantum mechanics. Found Phys 4, 127–136 (1974). https://doi.org/10.1007/BF00708563
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00708563