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Time-dependent response theory and nonequilibrium free-energy relations
Stephen R Williams1, Denis J Evans
1Research School of Chemistry, The Australian National University, Canberra, ACT 0200, Australia. swilliams@rsc.anu.edu.au
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
We derived a practical method for calculating the nonlinear response of classical systems to time-dependent fields. This advances computational simulations and experimental applications in statistical mechanics.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
- Computational Physics
Background:
- Time-dependent nonlinear response theory often yields complex, intractable results.
- Experimental and computational applications require simplified, applicable theoretical frameworks.
Purpose of the Study:
- To rigorously derive a tractable expression for nonlinear response in classical many-body systems.
- To connect nonlinear response theory with nonequilibrium free-energy relations.
Main Methods:
- Derivation of a closed-form expression for thermostatted nonlinear response.
- Analysis of systems subjected to time-dependent dissipative fields.
- Incorporation of concurrent parametric transformation of the system Hamiltonian.
Main Results:
- A mathematically rigorous and computationally feasible expression for nonlinear response was obtained.
- The intimate relationship between Jarzynski equality and nonlinear response theory was reaffirmed.
- The study provides a foundation for applying advanced theoretical concepts to practical problems.
Conclusions:
- The derived expression enhances the applicability of nonlinear response theory in simulations and experiments.
- This work bridges theoretical advancements with practical computational and experimental needs.
- Further exploration of the maximum entropy production approximation is suggested.
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