Usually in Brownian dynamics, we consider the Brownian particle size to be much-much larger than the size of the particles of the fluid on which the Brownian particle is immersed in. In this scenario the Langevin equation describes the motion of the Brownian particle. My doubt is, is it possible to apply Langevin equation onto a system were all the particles are of the same size (fluid particles as well as the Brownian particles) ?
The difference between the Langevin equation and Newton's equation is essentially the noise term representing the many collisions with the surrounding solvent. When one throws out the inertial term, one gets Brownian dynamics. Brownian dynamics is only valid when the length scales are much larger than the diameter of a typical solvent molecule. On shorter length scales (and corresponding time scales), the velocity autocorelation function is actually oscillatory (see fig 13). Using Brownian dynamics there is no autocorelation in the velocity. Even when one keeps the inertial term, the velocity autocorelation will be strictly positive, and not oscillatory. Of course you could probably achieve a reasonable velocity autocorelation function by throwing in a ton of particles, keeping the inertial term, and keeping the noise term relatively small. The better method would however be to use the Nose-Hoover thermostat (or some other thermostat for atomistic molecular dynamics).