A two-temperature linear spin model is presented as an introduction to nonequilibrium statistical physics. The model involves the concepts that are typical of more realistic nonequilibrium models, but has straightforward steady state solutions and, for small systems, development of the full time dependence for configuration probabilities. The model is accessible to upper-level undergraduates and provides a good check of computer models for larger systems.
REFERENCES
1.
J. W.
Gibbs
, Elementary Principles in Statistical Mechanics
(Scribner
, New York
, 1902
).2.
F.
Schmüser
and B.
Schmittmann
, “Nonequilibrium stationary state of a two-temperature spin chain
,” J. Phys. A
35
, 2569
–2580
(2002
).3.
L.
Boltzmann
, Lectures on Gas Theory
(U. California
, Berkeley, CA
, 1964
).4.
5.
R. K. P.
Zia
and B.
Schmittmann
, “Probability currents as principal characteristics in the statistical mechanics of nonequilibrium steady states
,” J. Stat. Mech.: Theory Exp.
P07012
, 1
–38
(2007
).6.
R. J.
Glauber
, “Time dependent statistics of the Ising model
,” J. Math. Phys.
4
, 294
–307
(1963
).7.
W.
Lenz
, “Die Wellenfunction und Verschwindigskeitverteilung des entarteten Gases
,” Z. Phys.
56
, 778
–789
(1929
).8.
E.
Ising
, “Beitrag zur Theorie des Ferromagnetismus
,” Z. Phys.
31
, 253
–258
(1925
).9.
Z.
Racz
and R. K. P.
Zia
, “Two-temperature kinetic Ising model in one dimension: Steady-state correlations in terms of energy and energy flux
,” Phys. Rev. E
49
, 139
–144
(1994
).10.
M.
Mobilia
, B.
Schmittmann
, and R. K. P.
Zia
, “Exact dynamics of a reaction-diffusion model with spatially alternating rates
,” Phys. Rev. E
71
, 056129
–1
(2005
).11.
K.
Binder
and D. W.
Heermann
, Monte Carlo Simulations in Statistical Physics
(Springer
, Berlin
, 1988
).12.
A fuller discussion of the role of the detailed balance condition can be found in the work of Zia and Schmittmann (Ref. 5).
© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.