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I am trying to warp my head around Monte Carlo simulations. To be exact, I am trying to figure to understand how you can use grand canonical Monte Carlo simulation of Lennard-Jones fluid to calculate the pressure at given temperature T and reduced density.

The Lennard-Jones potential dependance on distance between molecules looks like this: $$ V(r) = 4\varepsilon \left[\left(\frac{\sigma}{r}\right)^{12}−\left(\frac{\sigma}{r}\right)^{6}\right], $$ where $\varepsilon$ and $\sigma$ are constants specific to the gas in question.

How can I go from this equation to the pressure output from the Monte Carlo simulation? I have a program in possession (which I don't understand) that performs this calculation, but it is too long to paste it here.

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Not sure exactly what you are expecting to do.. but first and foremost, you must actually run the simulation and collect all relevant information about your particles. Then you may use that data to either directly calculate pressure or calculate easier physical quantities and relate it to pressure via thermodynamics.

Now if you don't understand what your simulation is doing, its going to be hard getting results and explaining them to others. As a "$0$th-step", I'd suggest learning how Monte Carlo simulations work, then try to read the one you have.

Please edit your question with an explanation of what you have attempted to do.

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