Dynamics for nonconservative systems: ergodicity beyond the microcanonical ensemble

Journal Article · Thu Jun 02 04:00:00 EDT 1988 · J. Phys. Chem.; (United States)

DOI:https://doi.org/10.1021/j100322a027· OSTI ID:6333305

Jellinek, J

A generalization of the procedure suggested recently by Nose for dynamical simulation of a canonical ensemble is presented. It is shown that there are infinitely many different dynamics capable of mimicking the canonical ensemble for a physical system provided the corresponding dynamics for an extended system consisting of the physical system and a bath is ergodic in a particular sense. An invariance property of ergodicity under scaling of the time is established. It is shown how the time scaling can be used to tune the dynamics into ergodicity with respect to any desired distribution function in a given phase space. The dynamics of the extended system implies an apparent trajectory for the physical system which is quite different from the one generated by the Hamiltonian dynamics for a closed physical system. A general unified scheme for dynamical simulation of any statistical mechanical ensemble is formulated.

• Research Organization: Argonne National Lab., IL (USA)
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 6333305
• Journal Information: J. Phys. Chem.; (United States), Journal Name: J. Phys. Chem.; (United States) Vol. 92:11; ISSN JPCHA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
DIFFERENTIAL EQUATIONS
DYNAMICS
EQUATIONS
EQUATIONS OF MOTION
ERGODIC HYPOTHESIS
HAMILTONIANS
HYPOTHESIS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
QUANTUM OPERATORS
SPACE
STATISTICAL MECHANICS