论文标题
被动和主动系统的耗散功能的属性
Properties of the dissipation functions for passive and active systems
论文作者
论文摘要
系统的耗散函数被定义为轨迹概率与其时间转换轨迹之间比率的自然对数，其概率分布遵循称为波动定理的众所周知的关系。使用通用langevin方程，我们得出被动和活动系统的耗散函数的表达式。对于被动系统，耗散函数仅取决于系统动力学变量的初始值和最终值，而不取决于系统的轨迹。此外，它不明确取决于通用兰格文鸟方程的反应性或耗散耦合系数。此外，我们在数值上研究了1D病例，以使用我们获得的耗散函数的形式验证波动定理。对于主动系统，我们定义了沿轨迹的主动力所做的工作。如果在时间逆转下，动态变量的概率分布是对称的，则在这两种情况下，随着轨迹持续时间的耗散函数的平均变化率不过是系统和储层的平均熵生产率。
The dissipation function for a system is defined as the natural logarithm of the ratio between probabilities of a trajectory and its time-reversed trajectory, and its probability distribution follows a well-known relation called the fluctuation theorem. Using the generic Langevin equations, we derive the expressions of the dissipation function for passive and active systems. For passive systems, the dissipation function depends only on the initial and the final values of the dynamical variables of the system, not on the trajectory of the system. Furthermore, it does not depend explicitly on the reactive or dissipative coupling coefficients of the generic Langevin equations. In addition, we study a 1D case numerically to verify the fluctuation theorem with the form of the dissipation function we obtained. For active systems, we define the work done by active forces along a trajectory. If the probability distribution of the dynamical variables is symmetric under time reversal, in both cases, the average rate of change of the dissipation function with trajectory duration is nothing but the average entropy production rate of the system and reservoir.
