Thermal motion thermodynamically coupled

From a thermodynamic point of view, molecular dynamics samples the microcanon-ical ensemble. In order to incorporate canonical thermal fluctuations by coupling the polymer system to a heat bath of canonical temperature T by means of a thermostat, Newton s equations of motion must be modified. Not the system energy E has to be constant, but the canonical expectation value ( ) at the given temperature. Thus, the task of the thermostat is twofold to keep the temperature constant and to sample the thermal... 

In the case of Nose-Hoover, this problem was known to both of the inventors and has been observed by many authors (see e.g. [251] and [180]). More recently, it has been studied analytically [218], Some confusion arises from the fact that the practical ergodic properties (and other properties) in Nosd-Hoover simulations are sensitive to the particular system under study and the values of parameters. For example it is known that in the case of simple liquids and gases, Nos6-Hoover does (at least under some conditions) enable reliable calculation of thermodynamical quantities [77], whereas in other systems results are poor and cannot be rectified by adjustment of parameters. In general, the control of temperature requires that the thermostat couples tightly to the physical variables, which generally calls for a small thermal mass, but this may be at odds with efficiency reduction (it may lead to a need to use smaller timesteps to resolve the motion of the auxiliary variable). 

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