We derive an exact expression for the probability density of work done on a particle that diffuses in a parabolic potential with a stiffness varying by an arbitrary piecewise constant protocol. Based on this result, the work distribution for time-continuous protocols of the stiffness can be determined up to any degree of accuracy. This is achieved by replacing the continuous driving by a piecewise constant one with a number n of positive or negative steps of increasing or decreasing stiffness. With increasing n , the work distributions for the piecewise protocols approach that for the continuous protocol. The moment generating function of the work is given by the inverse square root of a polynomial of degree n , whose coefficients are efficiently calculated from a recurrence relation. The roots of the polynomials are real and positive (negative) steps of the protocol are associated with negative (positive) roots. Using these properties the inverse Laplace tran...

中文翻译：

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统计光镊的刚度随时间变化的功数

我们得出一个精确的表达式，表示在粒子上以抛物线势扩散的刚度的工作概率密度，该刚度随任意分段常数协议而变化。基于此结果，可以确定刚度的时间连续方案的功分布，直至达到任何精度。这可以通过用连续n个增加或减少刚度的正数或负数步长代替分段恒定的连续驱动来实现。随着n的增加，分段协议的工作分配接近连续协议的工作分配。功的力矩生成函数由次数为n的多项式的反平方根给出，其系数可以根据递归关系有效地计算。多项式的根是实数，协议的正（负）步与负（正）根相关。使用这些属性，逆Laplace变换...