What can we learn from thermodynamics on stochastic dynamics? (Q2722390)

A thermodynamic approach to systems undergoing a pitchfork bifurcation and subjected to stochastic perturbation and a weak periodic forcing is developed as an example of the Schlögl autocatalytic reaction model for an ideal mixture. The entropy is defined in terms of the order parameter and its balance equation is derived. An information analog of the entropy production is introduced in the case of stochastic perturbation of a Gaussian white noise type. As a result, a link between thermodynamic-like quantities and the indicators of the complexity of the underlying dynamics is established. It is shown that bifurcation is reflected by the creation of one bit of information entropy. In the vicinity of stochastic resonance the intrinsic uncertainty is substantially lowered. The thermodynamic entropy production exhibits a great sensitivity toward the periodic forcing.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00031].