论文标题
在对称和不对称过程中的不可逆作品的扰动扩展
Perturbative expansion of irreversible works in symmetric and asymmetric processes
论文作者
论文摘要
Fokker-Planck方程解的系统扩展方法是通过概括[J.物理。 A50，325001（2017）]。使用此方法，我们获得了一个新公式来计算平均工作，该公式适用于Fokker-Planck运算符特征值中具有脱落性的系统。这种方法使我们能够研究几何对称性如何影响布朗粒子的热力学描述。为了说明派生理论的应用，我们考虑具有二维谐波电位的Fokker-Planck方程。为了研究电势对称的影响，我们研究了电势的对称和不对称变形过程中的热力学特性：谐波电位的旋转对称性在前者中保持，但后者在后者中被损坏。这些过程中优化的变形是通过最大程度地减少平均作品来定义的。比较这些优化的过程，我们发现，当电势的变形时间由关键时间给出时，对称过程和不对称过程之间的差异将最大化，而关键时间以Fokker-Planck方程的松弛时间为特征。平均工作中的关键时间小于平均能量变化的关键时间，因为不可逆的过程中的磁滞效应。
The systematic expansion method of the solution of the Fokker-Planck equation is developed by generalizing the formulation proposed in [J. Phys. A50, 325001 (2017)]. Using this method, we obtain a new formula to calculate the mean work perturbatively which is applicable to systems with degeneracy in the eigenvalues of the Fokker-Planck operator. This method enables us to study how the geometrical symmetry affects thermodynamic description of a Brownian particle. To illustrate the application of the derived theory, we consider the Fokker-Planck equation with a two-dimensional harmonic potential. To investigate the effect of symmetry of the potential, we study thermodynamic properties in symmetric and asymmetric deformation processes of the potential: the rotational symmetry of the harmonic potential is held in the former, but it is broken in the latter. Optimized deformations in these processes are defined by minimizing mean works. Comparing these optimized processes, we find that the difference between the symmetric and asymmetric processes is maximized when the deformation time of the potential is given by a critical time which is characterized by the relaxation time of the Fokker-Planck equation. This critical time in the mean work is smaller than that of the change of the mean energy because of the hysteresis effect in the irreversible processes.
