Abstract
This work is in line with new approaches for obtaining and studying non-Gibbs equilibrium distributions. Based on the Ising model, a new equilibrium distribution is obtained for the case of a thermostat that is commensurate with the system. It is also shown that the equilibrium distribution significantly deviates from the Gibbs distribution when the thermostat is smaller or commensurate with a separated system and tends to the Gibbs distribution in the limit of a large thermostat.
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REFERENCES
I. A. Kvasnikov, Thermodynamics and Statistical Physics, Vol. 2: Theory of Equilibrium Systems (URSS, Moscow, 2002) [in Russian].
R. Feinman, Statistical Mechanics (Benjamin, Massachusetts, 1972).
L. D. Landau and E. M. Livshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Fizmatlit, Moscow, 2002; Pergamon, Oxford, 1980).
J. W. Gibbs, Elementary Principles of Statistical Mechanics (Ox Bow Press, Woodbridge, 1981).
N. N. Bogolyubov, Selected Works, in 3 Volumes (Naukova Dumka, Kiev, 1970), Vol. 2, p. 297 [in Russian].
V. V. Kozlov, Poincaré and Gibbs Thermal Equilibrium (Moscow, 2002), p. 38 [in Russian].
E. W. Montroll and M. F. Shlesinger, J. Stat. Phys. 32, 209 (1983).
P. Bak, How Nature Works. The Science of Self-Organized Criticality (Springer, Berlin, 1996).
A. Renyi, Probability Theory (North-Holland, Amsterdam, 1970).
C. Tsallis, J. Stat. Phys. 52, 479 (1988).
A. G. Bashkirov and A. D. Sukhanov, J. Exp. Theor. Phys. 95, 440 (2002).
G. Wilk and Z. Wlodarczyk, Phys. Rev. Lett. 84, 2770 (2000).
C. Beck and E. G. D. Cohen, Phys. A (Amsterdam, Neth.) 322, 267–275 (2003).
D. Ramshaw John, Phys. Rev. E 98, 020103(R) (2018).
H. Hasegawa, Phys. Rev. E 83, 021104 (2011).
E. Ising, ‘‘Beitrag zur Theorie des Ferro- und Paramagnetismus,’’ Ph. D. Thesis (Univ. of Hamburg, 1924).
E. Ising, ‘‘Beitrag zur Theorie des Ferromagnetismus,’’ Z. Phys. 31, 253 (1925).
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Translated by E. Smirnova
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Ilin, P.K., Koval, G.V. & Savchenko, A.M. A Non-Gibbs Distribution in the Ising Model. Moscow Univ. Phys. 75, 415–419 (2020). https://doi.org/10.3103/S0027134920050148
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DOI: https://doi.org/10.3103/S0027134920050148