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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
