Tuesday 24 March 2020

thermodynamics - In a Monte Carlo $NVT $simulation how do I determine equilibration?


I'm running an NVT (constant number of particles, volume and temperature) Monte Carlo simulation (Metropolis algorithm) of particles in two dimensions interacting via Lennard-Jonse potential ($U = 4(\frac{1}{r^{12}} - \frac{1}{r^6})$, in reduced units). boundary conditions are periodic.


From this simulation I'm calculating the instantaneous pressure and potential energy. in the first steps the system is not in equilibrium, so I need to start averaging after the system is in equilibrium.


I'm starting my simulation from a random configuration.


My question: even after the system has reached equilibrium, it fluctuates around this equilibrium. these fluctuations may be large for large temperatures. so how do I know that I have reached equilibrium?


Here are some examples of the curve: The energy Vs. simulation step, for a high temperature (warmer color is higher density)


$$\uparrow$$ The energy Vs. simulation step, for a high temperature (warmer color is higher density)
The energy Vs. simulation step, for a low temperature (warmer color is higher density)



$$\uparrow$$The energy Vs. simulation step, for a low temperature (warmer color is higher density) The energy Vs. simulation step, for a high temperature, only for low densities. in this graph it's harder to tell if we reached equilibrium (warmer color is higher density)


$$\uparrow$$The energy Vs. simulation step, for a high temperature, only for low densities. in this graph it's harder to tell if we reached equilibrium (warmer color is higher density)




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