Departamento de Física, Universidade Federal de Santa Catarina, Campus Universitário, Trindade, 88040-900, Florianópolis, Santa Catarina, Brazil.
Departamento de Física, I3N, Universidade de Aveiro, 3810-193, Aveiro, Portugal.
Phys Rev E. 2018 Apr;97(4-1):042121. doi: 10.1103/PhysRevE.97.042121.
In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.
本文确定了作用在伊辛模型上的非平衡磁功，并将其与几年前 Jarzynski 推导出的涨落定理联系起来。该定理的基本思想是连接系统两个热力学态之间的自由能差与外部代理在有限时间内通过相同热力学态之间的非平衡路径执行的平均功之间的关系。我们通过考虑一维伊辛模型来检验这个定理的有效性，在该模型中，自由能作为温度和磁场的函数可以精确地确定。我们发现，Jarzynski 定理对于施加到系统上的磁场变化率的所有值都是有效的。我们还确定了正向和反向过程中系统上执行的功的概率分布函数，并验证了基于 Crooks 关系的预测同样正确。我们还提出了一种基于宏观变量计算系统与平衡状态之间滞后的方法。我们已经表明，在反向过程中，滞后随着场的最终值的扫掠速率而增加，而在正向过程中，滞后则减小。滞后与链的大小呈线性关系，斜率随场变化率的倒数减小。
