Langevin thermostat

The Langevin thermostat maintains the temperature through a modification of Newton's equations of motion

$\dot{r_i} = p_i/m_i \qquad \dot{p_i} = F_i - {\gamma}_i\,p_i + f_i,$

where F_i is the force acting on atom i due to the interaction potential, γ_i is a friction coefficient, and f_i is a random force simulating the random kicks by the damping of particles between each other due to friction. The random numbers are chosen from a Gaussian distribution with the following variance

$\sigma_i^2 = 2\,m_i\,{\gamma}_i\,k_B\,T/{\Delta}t$

with Δt being the time-step used in the MD to integrate the equations of motion. Obviously, Langevin dynamics is identical to the classical Hamiltonian in the limit of vanishing γ.

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