In a typical molecular dynamics and Monte Carlo simulation, we simulate a system under a fixed temperature (and pressure, etc.). The result is a trajectory of many configurations.
Now let us ask the inverse problem: given a trajectory from some unknown simulation, can we guess the simulation condition such as temperature and pressure? The answer is yes, provided we know the potential energy function of the system.
The key concept is the so-called configuration temperature (Rugh, Butler et al., Jepps et al.), which is computed from configuration averages. The formulas are related to the equipartition theorem and are limited to continuous systems. Now can we generalize configuration temperature to discrete systems? This project is such an attempt which relates the configuration temperature to a class of fluctuation theorems (Bochkov and Kuzovlev, Jarzynski).
Consider a classic system with a known potential energy U. If we randomly but evenly perturb configurations from a sufficiently long trajectory, the average potential change ⟨ ΔU ⟩ is always positive. Further, the ratio of the above average to the variance of the potential energy change ⟨ ΔU2 ⟩ roughly gives half of the inverse temperature β = 1/(kT). The simple formula, of course, requires some small modifications to be applicable to different ensembles.
As the application, the above result can be extended to compute a mean force, which is the derivative of a logarithmic distribution density. In such an application, we do not have to employ artificial perturbations, because the intrinsic fluctuation from natural time evolution can be used as such perturbations. From the mean force, we can inversely deduce a distribution, which is valuable for molecular simulations.
| Program | Description |
|---|---|
| rptprog.zip | Examples code in the paper (Zhang 2013). |