布朗旋轉子的製備是二維布朗粒子在諧和位能(harmonic potential)中，並受到來自不同方向且具備不同溫度的隨機力撞擊。我們將諧和位能替換為其他類型的位能，並通過模擬研究其非平衡穩態動力學(non-equilibrium steady state dynamics)。在非諧位能的情況下，我們發現此系統機率流(probability flow)不沿著機率等高線流動。甚至在可線性近似的位能低點附近也存在違反此特徵的情況。此現象意味著機率流的方向不垂直於機率梯度，且粒子的熵隨穩態軌跡而改變。;Electric circuits affected by thermal agitation are analog to confined Brownian particles in a high-viscosity fluid. Here we experimentally demonstrate an effective technique of generating tunable potentials for the Brownian dynamics in an electric circuit, realized by external controlled feedback. The thermal fluctuation undergoes equivalent Brownian dynamics in the authentic potentials as long as the feedback is fast enough to react for designed potentials. The results show that the electric-circuit version of feedback-trap provides a simple, effective, and programmable scheme to study non-equilibrium system. The generation can in principle be expanded to systems with multi degrees of freedom. The phenomenon of the Brownian gyrator can be observed by coupling two RC circuits with a feedback function instead of a coupling capacitor.
A Brownian gyrator features a two-dimensional random particle under a harmonic potential, while random thermal kicks are of distinct temperatures along the two orthogonal axes. We replace the harmonic potential by other types of potentials, and we investigate the non-equilibrium steady states through simulation studies. In contrast to the Brownian-gyrator case, where the probability flow circulates along the probability contour, the results for the non-harmonic cases do not follow this signature. Moreover, the violation of this feature exists even near the potential minima, where the harmonic approximation work. This implies that the probability flow is not perpendicular to the probability gradient and the entropy of the particle changes along with the steady state trajectory.
