# Better than counting: Density profiles from force sampling

D. de las Heras, and M. Schmidt

Phys. Rev. Lett., **120**, 218001, (2018) DOI: 10.1103/PhysRevLett.120.218001

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**Abstract**:

Calculating one-body density profiles in equilibrium via particle-based simulation methods involves
counting of events of particle occurrences at (histogram-resolved) space points. Here, we investigate an
alternative method based on a histogram of the local force density. Via an exact sum rule, the density profile
is obtained with a simple spatial integration. The method circumvents the inherent ideal gas fluctuations.
We have tested the method in Monte Carlo, Brownian dynamics, and molecular dynamics simulations. The
results carry a statistical uncertainty smaller than that of the standard counting method, reducing therefore
the computation time.

**Additional material/comments**:

**You can do better than just counting**

How many particles are there at a given point in space? The answer is given by the density profile, one of the most important quantities in Statistical Physics. Traditionally, the density profile is measured experimentally, or calculated in computer simulations, by literally counting the number of particles in each bin of a predefined spatial grid. We demonstrate here that one can do better than just counting. By sampling the forces acting on each particle, instead of only the position of the particle, it is possible to reconstruct the density profile. The result significantly improves the traditional counting method.

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