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Published on: March 30, 2017
Finite-precision stationary states at and away from equilibrium
1Department of Chemistry, University of Rochester, Rochester, New York 14627-0216, USA.
Summary
Finite computational precision affects dynamical systems by altering phase-space distribution fractions, particularly in dissipative systems. A new stochastic model explains these effects and links periodic orbit lengths to correlation dimension.
Area of Science:
- Statistical mechanics
- Dynamical systems theory
- Computational physics
Background:
- Understanding the impact of computational limitations on simulating complex systems is crucial.
- Phase-space distribution functions are key to characterizing system dynamics.
- Finite precision in simulations can introduce artifacts and alter results.
Purpose of the Study:
- To investigate how finite computational precision influences equilibrium and nonequilibrium phase-space distributions.
- To differentiate the effects of precision on conservative versus dissipative dynamical systems.
- To develop a model explaining the observed precision-dependent behaviors.
Main Methods:
- Numerical simulations of time-reversible dynamical systems with varying computational precision.
- Analysis of equilibrium and nonequilibrium phase-space distribution functions.
- Development and validation of a stochastic model against simulation results.
Main Results:
- Finite precision significantly alters the phase-space fraction occupied by distributions.
- Dissipative systems exhibit substantially reduced period lengths compared to conservative systems under finite precision.
- The convergence of thermodynamic averages is minimally affected by finite precision.
- A proposed stochastic model accurately predicts numerical findings.
Conclusions:
- Computational precision is a critical factor influencing the phase-space dynamics of simulated systems.
- The developed stochastic model provides a theoretical framework for understanding precision effects.
- The model establishes a connection between periodic orbit lengths and the correlation dimension of strange attractors.
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