Abstract
We present formulas for the Vasserstein distance between two statistical mechanical states of a two-state system. For example, in a ferromagnetic spin-1/2 Ising model the Vasserstein distance is half the difference in the magnetizations.
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References
L. N. Vasserstein,Problemy Peredachi Informatsii 5:64–73 (1969).
S. T. Rachev,Theory Prob. Appl. 29:647–676 (1985).
R. L. Dobrushin and S. B. Shlosman, inStatistical Physics and Dynamical Systems, J. Fritz, A. Jaffe, and D. Szász, eds. (Birkhauser, New York, 1985), pp. 347–403.
R. L. Dobrushin, J. Kolafa, and S. B. Shlosman,Commun. Math. Phys. 102:89–103 (1985).
D. C. Radulescu and D. F. Styer,J. Stat. Phys. 49:281–295 (1987).
R. Holley,Commun. Math. Phys. 36:227–231 (1974).
T. M. Liggett,Interacting Particle Systems (Springer-Verlag, New York, 1985), Section II.2.
A. B. Kirillov, A study of uniqueness of Gibbs states in the Ising model using the Dobrushin-Shlosman criterion, preprint, Academy of Sciences, USSR, Pushchino (1987).
G. Hansel, inThéorie Ergodique, A. Dold and B. Eckmann, eds. (Springer-Verlag, Berlin, 1976), pp. 143–151.
C. J. Preston,Commun. Math. Phys. 36:233–241 (1974).
V. Strassen,Ann. Math. Stat. 36:423–439 (1965).
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Kirillov, A.B., Radulescu, D.C. & Styer, D.F. Vasserstein distances in two-state systems. J Stat Phys 56, 931–937 (1989). https://doi.org/10.1007/BF01016786
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DOI: https://doi.org/10.1007/BF01016786