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Cell Gas Free Energy as an Approximation of the Continuous Model

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DOI: 10.4236/jmp.2015.62022    1,990 Downloads   2,307 Views   Citations

ABSTRACT

A continuous infinite system of point particles interacting via two-body strong superstable potential is considered in the framework of cell gas (CG) model of classical statistical mechanics. We consider free energy of this model as an approximation of the correspondent value of the continuous system. It converges to the free energy of the conventional continuous gas if the parameter of approximation α0 for any values of an inverse temperature β0 and volume per particle ν0.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Boluh, V. and Rebenko, A. (2015) Cell Gas Free Energy as an Approximation of the Continuous Model. Journal of Modern Physics, 6, 168-175. doi: 10.4236/jmp.2015.62022.

References

[1] Huang, K. (1963) Statistical Mechanics. John Wiley and Sons, Inc., London.
[2] Berezin, F.A. and Sinai, Ya.G. (1967) Transactions of the Moscow Mathematical Society, 17, 197-212.
[3] Dobrushin, R.L. (1967) Berk. Sym. Mat. Stat. Prob., VII, 73-87.
[4] Rebenko, A.L. (2013) Reviews in Mathematical Physics, 25, 1-28.
[5] Rebenko, A.L. and Tertychnyi, M.V. (2007) Proc. Inst. Math. NASU, 4, 172-182.
[6] Rebenko, A.L. and Tertychnyi, M.V. (2009) Journal of Mathematical Physics, 50, 0333301-033310. arXiv:0901.0826
[7] Petrenko, S.M., Rebenko, A.L. and Tertychnyi, M.V. (2010) Ukrainian Mathematical Journal, 63, 425-440.
arXiv:1007.4325
[8] Albeverio, S., Kondratiev, Yu.G. and Rockner, M. (1998) Journal of Functional Analysis, 154, 444-500.
http://dx.doi.org/10.1006/jfan.1997.3183
[9] Rebenko, A.L. (2014) Proc. Inst. Math. NASU, 11, 257-315.
[10] Ruelle, D. (1970) Communications in Mathematical Physics, 18, 127-159.
http://dx.doi.org/10.1007/BF01646091
[11] Ruelle, D. (1963) Helvetica Physica Acta, 36, 183-197.
[12] Ruelle, D. (1969) Statistical Mechanics (Rigorous Results). W.A. Benjamin, Inc., Amsterdam.
[13] Rebenko, A.L. and Tertychnyi, M.V. (2008) Methods of Functional Analysis and Topology, 14, 287-296.
[14] Park, Y.M. (1984) Communications in Mathematical Physics, 94, 1-33.
http://dx.doi.org/10.1007/BF01212347
[15] Dobrushin, R.L. (1964) Teoriya Veroyatnostei i ee Primeneniya, IX, 626-643.
[16] Dobrushin, R.L. and Minlos, R.A. (1967) Teoriya Veroyatnostei i ee Primeneniya, XII, 595-618.

  
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