What's the difference between Brownian dynamics and molecular dynamics? Are they any correlations between them?
Although the information given in two previous answers is overall correct, there is a little of confusion about how molecular, Langevin and Brownian dynamics relate to each other. In fact, Langevin dynamics provide a general theoretical frame to two others. The Langevin equation of motion consists of three terms: 1) forces arising from interactions with other particles, 2) forces arising from momenta inherited from the previous time step (this term contains a damping multiplier that accounts for viscosity of the medium), and 3) random forces. All three terms might be useful in molecular dynamics, because MD is not only about moving particles of interest, but also maintaining constant temperature and pressure or imitating a solvent. Then, if in term (2) the damping constant would be large enough, then momenta from the previous step (inertia) would not contribute to the motion anymore. This special case would be called overdamped Langevin dynamics or Brownian dynamics.
Using molecular dynamics implies solving Newton equations of motion
for many-particle system. E.g., the system configuration
at a certain time point is obtained as the result of solving
system of ordinary differential equations of second order,
for coordinates and impulses.
Brownian dynamics (which is oftenly referred to as Langevin dynamics as well)
deals with systems embedded in thermostat. This means that, along with
regular interparticle potential forces, two additional type of forces
acting on particles have to be taken into account, the friction and stochastic
(Langevin) forces. In the case that the observation time is long or
the friction is strong, the Langevin equations reduce to the overdamped case
where only the coordinates of particles are present. In this limiting case
the inertial forces are neglected and
it is assumed that the velocity distribution is Maxwellian and the averaging
over velocities is already performed. This overdamped case is also referred to
as Brownian dynamics. In thermal equilibrium, the results obtained within these
3 approaches should be identical. For nonequilibrium processes,
BD describes the relaxation of as system embedded in thermostat to thermal equilibrium.
Molecular dynamics is a simulation method for studying the physical movements of atoms and molecules. On the other hand, Brownian dynamics can be used to describe the motion of molecules since it is a simplified version of Langevin dynamics.
I think you can find an interesting first reading in https://en.wikipedia.org/wiki/Langevin_dynamics#Overview
Although the information given in two previous answers is overall correct, there is a little of confusion about how molecular, Langevin and Brownian dynamics relate to each other. In fact, Langevin dynamics provide a general theoretical frame to two others. The Langevin equation of motion consists of three terms: 1) forces arising from interactions with other particles, 2) forces arising from momenta inherited from the previous time step (this term contains a damping multiplier that accounts for viscosity of the medium), and 3) random forces. All three terms might be useful in molecular dynamics, because MD is not only about moving particles of interest, but also maintaining constant temperature and pressure or imitating a solvent. Then, if in term (2) the damping constant would be large enough, then momenta from the previous step (inertia) would not contribute to the motion anymore. This special case would be called overdamped Langevin dynamics or Brownian dynamics.
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