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. 2019 Jan;99(1-1):012129. doi: 10.1103/PhysRevE.99.012129.
In this work we consider the nonequilibrium mechanical and magnetic work performed on a one-dimensional compressible Ising model. In the harmonic approximation we easily integrate the mechanical degrees of freedom of the model, and the resulting effective Hamiltonian depends on two external parameters, the magnetic field and the force applied along the chain. As the model is exactly soluble in one dimension we can determine the free energy difference between two arbitrary thermodynamic states of the system. We show the validity of the Jarzynski equality, which relates the free energy difference between two thermodynamic states of the system and the average work performed by external agents in a finite time, through nonequilibrium paths between the same thermodynamic states. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field and the mechanical force applied to the system.
在这项工作中，我们考虑了对一维可压缩伊辛模型所做的非平衡力学和磁学功。在简谐近似下，我们很容易对模型的力学自由度进行积分，得到的有效哈密顿量取决于两个外部参数，磁场和沿链施加的力。由于模型在一维是完全可解的，我们可以确定系统任意两个热力学态之间的自由能差。我们证明了雅可比等式的有效性，该等式通过同一热力学态之间的非平衡路径将系统两个热力学态之间的自由能差与外场在有限时间内所做的平均功联系起来。我们发现，对于磁场变化率和施加于系统的力学力的所有值，雅可比定理仍然有效。
