Batygolski Jerzy, Napierała-Batygolska Aleksandra, Lipowski Adam
Faculty of Physics, Adam Mickiewicz University, Poznań, Poland.
Phys Rev E. 2022 Jun;105(6-1):064120. doi: 10.1103/PhysRevE.105.064120.
Fluctuation relations of Jarzynski and Crooks enable efficient calculations of a free-energy difference between equilibrium states. In the present paper, we provide some numerical evidence that these relations can also be used for a two-dimensional Ising-doped voter model, which is a nonequilibrium system with a violated detailed balance. Adopting the method of Híjar and Sutmann, we implement a protocol that switches between periodic and antiperiodic boundary conditions and induces formation of an interface in the model. Assuming that a suitably interpreted Ising Hamiltonian can be considered as a pseudoenergy of the model, we examine fluctuations of work performed during these processes and estimate the surface tension. Our results confirm that the surface tension remains positive in this model except a limiting case of the voter model, where it seems to vanish. Comparing the free-energy estimates at different speeds of the switching process, we also estimate an effective temperature in the model. Perhaps coincidentally, the effective temperature of the voter model appears to be close to the critical temperature of the Ising model.
雅津斯基（Jarzynski）和克鲁克斯（Crooks）涨落关系能够高效计算平衡态之间的自由能差。在本文中，我们提供了一些数值证据，表明这些关系也可用于二维伊辛掺杂选民模型，这是一个违背细致平衡的非平衡系统。采用希贾尔（Híjar）和苏特曼（Sutmann）的方法，我们实现了一个在周期性和反周期性边界条件之间切换并诱导模型中界面形成的协议。假设一个经过适当解释的伊辛哈密顿量可被视为模型的赝能，我们研究这些过程中所做功的涨落并估计表面张力。我们的结果证实，在该模型中表面张力保持为正，但选民模型的一个极限情况除外，在该极限情况下表面张力似乎消失。通过比较不同切换过程速度下的自由能估计值，我们还估计了模型中的有效温度。也许巧合的是，选民模型的有效温度似乎接近伊辛模型的临界温度。
