Chaotic behavior in nonlinear Hamiltonian systems and equilibrium statistical mechanics

Journal Article · Sat Aug 01 04:00:00 EDT 1987 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01019687· OSTI ID:5264477

Livi, R; Pettini, M; Ruffo, S; Vulpiani, A

The relation between chaotic dynamics of nonlinear Hamiltonian systems and equilibrium statistical mechanics in its canonical ensemble formulation has been investigated for two different nonlinear Hamiltonian systems. The authors have compared time averages obtained by means of numerical simulations of molecular dynamics type with analytically computed ensemble averages. The numerical simulation of the dynamic counterpart of the canonical ensemble is obtained by considering the behavior of a small part of a given system, described by a microcanonical ensemble, in order to have fluctuations of the energy of the subsystem. The results for the Fermi-Pasta-Ulam model (i.e., a one-dimensional anharmonic solid) show a substantial agreement between time and ensemble averages independent of the degree of stochasticity of the dynamics. On the other hand, a very different behavior is observed for a chain of weakly coupled rotators, where linear exchange effects are absent. In the high-temperature limit (weak coupling) they have a strong disagreement between time and ensemble averages for the specific heat even if the dynamics is chaotic. This behavior is related to the presence of spatially localized chaos, which prevents the complete filling of the accessible phase space of the system. Localized chaos is detected by the distribution of all the characteristic Liapunov exponents.

• Research Organization: Universita degli Studi de Firenze (Italy)
• OSTI ID: 5264477
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 48:3/4; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COUPLING
CRYSTAL MODELS
ENERGY
EQUILIBRIUM
ERGODIC HYPOTHESIS
HAMILTONIANS
HYPOTHESIS
INTERMEDIATE COUPLING
J-J COUPLING
LYAPUNOV METHOD
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
NONLINEAR PROBLEMS
PHYSICAL PROPERTIES
POTENTIAL ENERGY
QUANTUM MECHANICS
QUANTUM OPERATORS
SPECIFIC HEAT
STATISTICAL MECHANICS
THERMODYNAMIC PROPERTIES
THERMODYNAMICS