论文标题
探索谐波振荡器的jarzynski平等
Exploring the Jarzynski Equality for the Harmonic Oscillator
论文作者
论文摘要
大约25年前，Jarzynski发表了一篇论文：W所做的工作是从状态A到状态B驱动系统的工作，其特征是Helmholtz Free Energies FA和FB，满足了一个平等，在该平均值中，平均测量合奏的平均值确定了自由能的差异。此结果的几个功能需要在文本中给出更多详细的描述。平等是重要的和出乎意料的。关于平等的说法也是如此，与几年前从状态A到州的变化率无关。这是由于时间尺度差异的巨大差异，以进行动量放松和坐标放松。 jarzynski平等（JE）将在此显示仅在慢速过程的极限中是正确的。提出的示例是用于带胡克弹簧常数K的大分子谐波振荡器，该弹簧常数K在时间间隔内从K1线性变为K2。缓慢执行时，我们以与K的比率相关的形式获得JE。但是，当过渡更快地进行过渡时，平等就会丢失。 Jarzynski向我建议，Hummer和Szabo表明JE直接来自Feynman-Kac公式。我们在这里表明，F-K不会重现本文中执行的直接计算，并且已经在早期论文中被滥用。
Almost 25 years ago, Jarzynski published a paper in which it was asserted: the work done, W, in driving a system from state A to state B, characterized by the Helmholtz free energies FA and FB, satisfies an equality in which an average over an ensemble of measurements for W determines the difference in Free energy. Several features of this result require more detailed description, to be given in the text. The equality is significant and unexpected. So is the statement that the equality is independent of the rate of change from state A to state B. A few years ago, I had presented three papers in which the contraction of the description from full phase space to coordinate space only was made. This was motivated by the large difference in time scales for momenta relaxation and coordinate relaxation. The Jarzynski equality (JE) will be shown here to be correct only in the limit of slow processes. The proposed example is for a macromolecular harmonic oscillator with a Hooke's spring constant, k, that during the time interval linearly changes from k1 to k2. When performed slowly, we obtain JE in a form in which the free energy is related to the ratio of the k's. However, when the transition is performed more rapidly the equality is lost. Jarzynski has suggested to me that Hummer and Szabo have shown that JE follows directly from the Feynman-Kac formula. We show here that F-K does not reproduce the direct calculation executed in this paper and that it has been misapplied in earlier papers.
