  In this work, a Josephson junction consisting of two superconducting layers
sandwiching an insulating layer is explored, which is subject to the effects of
thermal fluctuations. The precise expressions for the evolution of Josephson
phase and the supercurrent through the junction are derived. A clockwise
hysteresis cycle in the current-voltage characteristic curve is demonstrated
mathematically. Additionally, the bifurcation of a planar limit cycle is
established. The numerous stochastic thermodynamic properties of the
resistively shunted superconducting tunnel junction system are described,
considering the influence of three specific parameters: the conductance, the
current bias and the noise intensity. Moreover, the probability density is
characterized using the Fokker-Planck equation.
