q-thermostatistics of noise-driven Van der Pol oscillator

We study the noise-driven Van der Pol oscillator whose dissipative term yields stationary distributions of the q-exponential form. The thermostatistical observables such as internal energy and temperature are also calculated. Since this model depends on a control parameter which acts as a coupling parameter between the system and environment, the noise-driven Van der Pol oscillator also serves as a nice model where the interplay of both nonextensivity and open character of the system can be considered. We observe that the model behaves as if it is coupled to a finite heat bath for small values of control parameter. As the control parameter increases, the effect of the linear friction coefficient disappears, and the stationary distribution becomes a q-Gaussian, thereby breaking the coupling with the finite heat bath. Finally, we remark that negative temperature values are not observed contrary to an earlier analysis of a similar model. The elucidation of this point is commented in the framework of the misidentification of the correct form of the q-exponentials and the nonextensivity index q.