Editing Test volume method

The '''test volume method''' provides an alternative to the [[virial pressure]] route for calculating the  [[pressure]] of a system. This method  consists of
evaluating the change in [[internal energy]], <math>\Delta U</math> produced by a small change in the volume of the system, <math>\Delta V</math>.

This can be thought  of as a "blow-up" (or "in") of the whole system, <math>x \rightarrow (1+\alpha) x</math> with a small <math>\alpha</math> (similarly for <math>y</math> and <math>z</math>), exactly in the same way as the [[virial pressure]] expression may be derived, i.e.  not as leaving the particles in their places and changing the simulation cell (a procedure which does not make sense in general).

It can be shown that
:<math> p  =  \frac{ k_B T  N}{V} + \frac{ k_B T  }{ \Delta V } \log \langle \exp(-\Delta U/k_B T )\rangle,</math>
where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].
The method is clearly inspired by the [[ Widom test-particle method]], which is used to obtain the [[chemical potential]].
It has been argued that this method can be more useful than [[virial pressure]], since it avoids the calculation of forces (which are not needed in a [[Monte Carlo]] simulation). Moreover, there are interaction potentials that are [[Idealised models#Piecewise continuous models |discontinuous]]. In such cases the forces are not well defined, and one would have to  consider the limit of "almost-discontinuous" potentials instead, which can be cumbersome. However, it should be noted that it is not clear how to "blow up" a system containing molecules held by rigid constraints.
==References==
#[http://dx.doi.org/10.1063/1.472721   V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' pp. 8469- (1996)]
[[category: computer simulation techniques]]