Abstract
The Hertel-Thirring cell model for unstable systems (of purely attractive particles) is solved in the canonical ensemble for arbitrary dimensions. The differences between the phase transitions found in the canonical and in the microcanonical ensemble are discussed. The cluster phase (with a complete collapse in the ground state) exhibits the nonextensive character of the cell model. The results of the cell model are compared with molecular-dynamics simulations of a one-dimensional model with a rectangular-well pair potential. The simulations support the relevance of the cell model to characterize basic properties of gravitational systems.
Similar content being viewed by others
References
P. Hertel and W. Thirring, A soluble model for a system with negative specific heat,Ann. Phys. (N.Y.) 63:520 (1971).
A. Compagner, C. Bruin, and A. Roelse, Collapsing systems,Phys. Rev. A 39:5089 (1989).
M. K. H. Kiessling, On the equilibrium statistical mechanics of isothermal classical self-gravitating matter,J. Stat. Phys. 55:203 (1989).
H. A. Posch, H. Narnhofer and W. Thirring, Dynamics of unstable systems,Phys. Rev. A 42:1880 (1990); Externally perturbed systems,J. Stat. Phys. 65:555 (1991).
H. A. Posch, H. Narnhofer, and W. Thirring,Simulation of Complex Flows, M. Mareschal, ed. (Plenum Press, New York 1990), p. 291.
B. J. Alder and T. E. Wainwright, Studies in molecular dynamics. I. General method,J. Chem. Phys. 31(2):459 (1959).
W. G. Hoover and B. J. Alder, Studies in molecular dynamics. IV. The pressure, collision rate, and their number dependence for hard disks,J. Chem. Phys. 46(2):486 (1967).
J. L. Lebowitz, J. K. Percus, and L. Verlet, Ensemble dependence of fluctuations with applications to machine computations,Phys. Rev. 153:250 (1967).
S. D. Stoddard, Identifying clusters in computer experiments on systems of particles,J. Comp. Phys.,27:291 (1978).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bokhove, O., Bruin, C. & Compagner, A. Ensemble properties and molecular dynamics of unstable systems. J Stat Phys 74, 55–73 (1994). https://doi.org/10.1007/BF02186806
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02186806