I've been taught that when simulating a biomolecule in thermal equilibrium, it's best to use the Langevin thermostat - an algorithm which produces a trajectory, which is a realization of a stochastic process given by the Langevin (stochastic differential) equation. I haven't had a doubt about this algorithm's power to create a sample from the Boltzmann distribution, but what about it's correctness regarding time-dependent behaviour of the system? In other words: does the movie we get from a simulation reflect how biomolecules actually behave?Recently, I've been studying van Kampen's Stochastic Processes in Physics and Chemistry (3rd edition), where on page 56 (chapter III, paragraph 2.) there is a rather philosophical discussion of the stochastic description of microscopic systems. Here's the part that I found most confusing:Having accepted that the irregular motion of a system may be reformulated as a stochastic process, one is faced with the task of choosing the appropriate process. For a closed, isolated system that is usually done as follows. The microscopic deterministic motion may be represented by a trajectory in the phase space $\Gamma$. Each point $X\in\Gamma$ is, after a time $t$ mapped by the motion into a point $X^t\in\Gamma$, where $X^t = f(X,t)$ is uniquely determined. If one now chooses at some initial time $t=0$ not a single initial state $X$, but a probability density $P(x)$ in $\Gamma$, then $f(x,t)$ is a stochastic process as defined in the preceding section. The initial $P(x)$ is to be chosen so as to reflect the way in which the system was prepared. Any other physical quantity pertaining to the system is a function $Y(X^t)$ of the phase point $X^t$ and has therefore also become a stochastic process $Y(X,t)$.This is the usual approach to the stochastic description of nonequilibrium behavior and fluctuations. It is the starting point of the derivation of the so-called generalized Langevin equation and of the Kubo relations in linear response theory. It was even advocated in the first edition of this book -- but it is wrong. The irregular motion of a Brownian particle can not be related to a probability distribution of some initial state. Rather it is brought about by the surrounding bath molecules and is a vestige of all the variables of the total system that have been ignored in order to obtain an equation for the Brownian particle alone, see IV.a and VIII.3. The proper way of establishing the stochastic description of Brownian motion is therefore the careful elimination of the bath variables from the complete set of microscopic equations of the total system. (Van Kampen provides a reference: N.G. van Kampen and I Oppenheim, Physica A 138, 231 (1986), to which I haven't got access.)My question: is it then incorrect to use the Langevin thermostat when we are interested in the actual, time-dependant behaviour of a molecular system? Or, perhaps, the Langevin-equation-based description isn't that bad once we immerse the biomolecule in a sufficiently large water basin, thus emulating the complexity of the environment? 
Is Langevin thermostat/equation correct when trying to model time-dependent behaviour of a molecule?
molecular dynamics;stochastic