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Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method

1
Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
2
Physics Department, University of Trento, via Sommarive 14, I-38123 Trento, Italy
3
INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(4), 222; https://doi.org/10.3390/e20040222
Received: 1 March 2018 / Revised: 21 March 2018 / Accepted: 22 March 2018 / Published: 24 March 2018
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
The spatial block analysis (SBA) method has been introduced to efficiently extrapolate thermodynamic quantities from finite-size computer simulations of a large variety of physical systems. In the particular case of simple liquids and liquid mixtures, by subdividing the simulation box into blocks of increasing size and calculating volume-dependent fluctuations of the number of particles, it is possible to extrapolate the bulk isothermal compressibility and Kirkwood–Buff integrals in the thermodynamic limit. Only by explicitly including finite-size effects, ubiquitous in computer simulations, into the SBA method, the extrapolation to the thermodynamic limit can be achieved. In this review, we discuss two of these finite-size effects in the context of the SBA method due to (i) the statistical ensemble and (ii) the finite integration domains used in computer simulations. To illustrate the method, we consider prototypical liquids and liquid mixtures described by truncated and shifted Lennard–Jones (TSLJ) potentials. Furthermore, we show some of the most recent developments of the SBA method, in particular its use to calculate chemical potentials of liquids in a wide range of density/concentration conditions. View Full-Text
Keywords: computer simulations; finite-size effects; calculation of free energies; thermodynamic limit computer simulations; finite-size effects; calculation of free energies; thermodynamic limit
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Heidari, M.; Kremer, K.; Potestio, R.; Cortes-Huerto, R. Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method. Entropy 2018, 20, 222.

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