热流涨落稳态涨落定理的检验

曲靖师范学院学报 ›› 2022, Vol. 41 ›› Issue (6): 25-31.

热流涨落稳态涨落定理的检验

毕铭阳, 赵鸿

厦门大学物理科学与技术学院,福建厦门 361000

收稿日期:2022-07-11 出版日期:2022-11-26 发布日期:2022-12-14
通讯作者: 赵鸿,厦门大学物理科学与技术学院教授,主要从事统计物理与复杂系统研究.
作者简介:毕铭阳,厦门大学物理科学与技术学院硕士研究生,主要从事统计物理与复杂系统研究.
基金资助:
国家自然科学基金面上项目“基于当前数据的系统整体动力学行为预测理论和方法”(11975189).

Test of Steady-State Fluctuation Theorem on Heat Flux Fluctuation

BI Mingyang, ZHAO Hong

School of Physical Science and Technology, Xiamen University, Xiamen Fujian 361000, China

Received:2022-07-11 Published:2022-11-26 Online:2022-12-14

摘要/Abstract

摘要： 对涨落定理的研究是统计物理的前沿热点,检验稳态涨落定理的正确性以及探究其可应用的参数范围具有十分重要且现实的意义.研究了两端与不同温度朗之万热源接触的三类典型一维晶格模型中的热流涨落,并由此对稳态涨落定理进行了细致的检验.数值计算的结果显示,三类模型的热流涨落在测量时间窗口趋于无穷的极限情况下,稳态涨落定理都严格成立.研究发现,在有限测量时间窗口下,对涨落定理的偏离随着系统尺寸的增大而增大,但是不同系统尺寸的涨落关系存在一个尺度变换,可以很好地重整为一个普适的依赖关系,这意味着有限尺寸系统具有某种普适的涨落关系.同时还研究了涨落关系的非线性偏离.

关键词: 稳态涨落定理, 一维晶格模型, 非线性, 尺度率

Abstract: The research on fluctuation theorem is a topic of general interest in statistical physics, and it is of great importance and practical significance to verify the steady-state fluctuation theorem and investigate the applicable range of the parameters. In this article, we study three kinds of typical one-dimensional lattices models coupled with Langevin heat reservoirs at different temperature on both ends to carefully verify the steady-state fluctuation theorem. Numerical results show that all of the heat flux of three kinds of models strictly obey the steady-state fluctuation theorem when in the limit that the measure time window goes to infinity. The deviation of fluctuation theorem rising with the increase of the system size under the case of finite measure time window is found as well. There is a scaling change on different size of systems which can be good to rescale into a universal dependency. The nonlinear deviation of the fluctuation relation is also studied in this article.

Key words: steady-state fluctuation theorem, one-dimensional lattices model, nonlinear, scaling law

中图分类号:

O414.22

毕铭阳, 赵鸿. 热流涨落稳态涨落定理的检验[J]. 曲靖师范学院学报, 2022, 41(6): 25-31.

BI Mingyang, ZHAO Hong. Test of Steady-State Fluctuation Theorem on Heat Flux Fluctuation[J]. Journal of Qujing Normal University, 2022, 41(6): 25-31.

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