Cell Gas Free Energy as an Approximation of the Continuous Model

Vira A. Boluh¹, Alexei L. Rebenko^2*

¹Faculty of Mathematics, Zhytomyr, Ukraine.
²Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine.

DOI: 10.4236/jmp.2015.62022                

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 α→0 for any values of an inverse temperature β＞0 and volume per particle ν＞0.

Keywords

Strong Superstable Potential, Quasi-Lattice Approximation, Cell Gas

Conflicts of Interest

The authors declare no conflicts of interest.

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.