Palmieri Benoit, Ronis David
Department of Chemistry, McGill University, 801 Sherbrooke Ouest, Montréal, Québec, Canada H3A 2K6.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jan;75(1 Pt 1):011133. doi: 10.1103/PhysRevE.75.011133. Epub 2007 Jan 31.
The one-dimensional expanding ideal gas model is used to compute the exact nonequilibrium distribution function. The state of the system during the expansion is defined in terms of local thermodynamics quantities. The final equilibrium free energy, obtained a long time after the expansion, is compared against the free energy that appears in the Jarzynski equality. Within this model, where the Jarzynski equality holds rigorously, the free energy change that appears in the equality does not equal the actual free energy change of the system at any time of the process. More generally, the work bound that is obtained from the Jarzynski equality is an upper bound to the upper bound that is obtained from the first and second laws of thermodynamics. The cancellation of the dissipative (nonequilibrium) terms that result in the Jarzynski equality is shown in the framework of response theory. This is used to show that the intuitive assumption that the Jarzynski work bound becomes equal to the average work done when the system evolves quasistatically is incorrect under some conditions.
一维膨胀理想气体模型用于计算精确的非平衡分布函数。膨胀过程中系统的状态是根据局部热力学量来定义的。将膨胀很久之后获得的最终平衡自由能与雅尔津斯基等式中出现的自由能进行比较。在该模型中，雅尔津斯基等式严格成立，等式中出现的自由能变化在过程的任何时刻都不等于系统的实际自由能变化。更一般地说，从雅尔津斯基等式得到的功的界限是从热力学第一和第二定律得到的界限的上限。在响应理论的框架下展示了导致雅尔津斯基等式的耗散（非平衡）项的抵消。这用于表明在某些条件下，认为当系统准静态演化时雅尔津斯基功的界限等于平均功的直观假设是不正确的。
