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Communication: Pressure fluctuations in isotropic solids and fluids
1. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954).
2. H. B. Callen, Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1985).
3. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, 1995).
4. J. S. Rowlinson, Liquids and Liquid Mixtures (Butterworths Scientific Publications, London, 1959).
8. M. Allen and D. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1994).
11.That Eq. (13) becomes exact for V → ∞ can be also seen by using that the distribution of is Gaussian.
12.For the excess pressure fluctuations a similar relation is obtained using Eq. (9) together with Eqs. (11) and (12). This relation has been also confirmed numerically.
13.In d = 1 “volume” corresponds to the linear length of the system and in d = 2 to its surface. Pressure and elastic moduli take units of energy per d-dimensional volume.
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Comparing isotropic solids and fluids at either imposed volume or pressure, we investigate various correlations of the instantaneous pressure and its ideal and excess contributions. Focusing on the compression modulus K, it is emphasized that the stress fluctuation representation of the elastic moduli may be obtained directly (without a microscopic displacement field) by comparing the stress fluctuations in conjugated ensembles. This is made manifest by computing the Rowlinson stress fluctuation expression K row of the compression modulus for NPT-ensembles. It is shown theoretically and numerically that K row| P = P id(2 − P id/K) with P id being the ideal pressure contribution.
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