Multiparticle correlations, entropy of partial distributions, and the direct variational method. (English) Zbl 1178.82007
Theor. Math. Phys. 143, No. 1, 615-624 (2005); translation from Teor. Mat. Fiz. 143, No. 1, 150-160 (2005).
Summary: In the classical statistical theory, multiparticle correlations are governed by a variational principle for a functional that becomes the thermodynamic potential on its extremal. We show that this functional contains a part that has the meaning of a sum of contributions from multiparticle entropies. We present a method for passing from the conditional variational problem for the thermodynamic potential to an unconditional one.
MSC:
82B05 | Classical equilibrium statistical mechanics (general) |
62B10 | Statistical aspects of information-theoretic topics |
62H20 | Measures of association (correlation, canonical correlation, etc.) |
Keywords:
partial distributions; irreducible contributions; connected diagrams; entropy; direct correlations; total correlations; direct variational principleReferences:
[1] | E. A. Arinshtein, Theor. Math. Phys., 124, 972-981 (2000). · Zbl 0983.82004 · doi:10.1007/BF02551071 |
[2] | E. A. Arinshtein and R. M. Ganopol?skii, Theor. Math. Phys., 131, 681-689 (2002). · Zbl 1031.82040 · doi:10.1023/A:1015428932643 |
[3] | É. A. Arinshtein, Theor. Math. Phys., 141, 1461-1468 (2004). · Zbl 1178.82075 · doi:10.1023/B:TAMP.0000043861.74454.65 |
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