Noise perturbation of the thermostat in constant temperature molecular dynamics simulations

In this work we study the effects of noise applied on the thermostat in the case of the constant temperature molecular dynamics simulations. We consider the cases of additive and or multiplicative noise. We then examine the influence of the perturbed thermostat on the instantaneous temperature of the thermostated physical system. We introduce topological criteria and a formulation of the stability concept of a perturbed time series. The numerical investigation applied to the temperature time series of the physical system shows a strong stability under the application of additive noise while the application of multiplicative noise results in instability.