Dependence of the existence of thermal equilibrium on the number of particles at low temperatures

American Journal of Physics

Volumn 75, Issue 5, 2007, Pages 431-433

  Wang, X ^a   Liu, Q H ^a   Dong, W ^b  

^a HUNAN UNIVERSITY   (China)

^b UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547112916     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2432128     Document Type: Article

References (15)

1. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed. (Butterworth-Heinemann, Singapore, 1999), Chap. XII.
2. B. B. Mandelbrot, "Temperature fluctuations: A well-defined and unavoidable notion," Phys. Today, 42(1), 71-73 (1989) and references therein.
3. G. D. Phillies, "The polythermal ensemble: A rigorous interpretation of temperature fluctuations in statistical mechanics," Am. J. Phys. 52, 629-632 (1984). It is the first rigorous interpretation of temperature fluctuations from the perspective of the "polythermal" ensemble, which is an extension of the canonical ensemble consisting of a collection of canonical ensembles with different temperatures.
4. H. B. Prosper, "Temperature fluctuations in a heat bath," Am. J. Phys. 61, 54-58 (1993). This paper contains a practical method to calculate the temperature fluctuations within statistical mechanics.
5. J. X. Hou, X. Wang, S. Huang, J. J. Lin, C. L. Wan, and Q. H. Liu, "On the divergence problem of temperature fluctuations in simple systems," Acta Phys. Sin. 55, 1616-1621 (2006).
6. J. Uffink and J. van Lith, "Thermodynamic uncertainty relations," Found. Phys. 29, 655-692 (1999);
7. "Thermodynamic uncertainty relations again: A reply to Lavenda," Found. Phys. Lett. 14, 187-193 (2001);
8. B. H. Lavenda, "Comments on 'Thermodynamic uncertainty relations' by J. Uffink and J. van Lith," Found. Phys. Lett. 13, 487-492 (2000).
9. B. H. Lavenda, Statistical Physics: A Probabilistic Approach (Wiley, New York, 1991), p. 193.
10. -3 as given in Table I of this paper.
11. M. Hartmann, G. Mahler, and O. Hess, "Existence of temperature on the nanoscale," Phys. Rev. Lett. 93, 080402-1-4 (2004);
12. "Local versus global thermal states: Correlations and the existence of temperatures," Phys. Rev. E 70, 066148-1-12 (2004).
13. C. Kittel, "Temperature fluctuations: An oxymoron," Phys. Today 41(5), 93 (1988). Kittel argues that the temperature by its definition does not fluctuate at all. As an immediate response to Kittel's opinion, Mandelbrot reaffirmed his 1960s' assertion with the intention "to explain it to a wide audience." (Ref. 2)
14. x → 0 as T → 0 is a straightforward consequence of Nernst's theorem, which is one of the standard statements of the third law of thermodynamics.
15. K. Huang, Statistical Mechanics (Wiley, New York, 1987).