统计物理教学中引入Jarzynski等式的必要性
NECESSITY OF INTRODUCING JARZYNSKI EQUALITY IN STATISTICAL PHYSICS TEACHING
覃莉
摘要(Abstract)：
20世纪90年代以来,统计物理学界最重要的成果之一是Jarzynski在1997年得到的一个远离平衡态等式,称为Jarzynski等式。其具有广泛的适用性,且已经在单个DNA分子的实验上得到了证实和应用。Jarzynski等式具有重要的意义:利用该等式可以由非平衡物理过程中功的测量来精确地计算两个平衡态之间Helmholz自由能的差。本文简要综述了Jarzynski等式理论和实验的重要研究成果,表明Jarzynski等式是物理世界中一个非常本质的规律,进而阐明统计物理教材或教学的讨论课程中引入这一等式的必要性。
关键词(KeyWords)： Jarzynski等式;统计物理;教学
基金项目(Foundation): 西北农林科技大学2017年教学改革研究项目“适应学生学科背景的《大学物理》教学内容优化及相应教学方法的研究”资助
作者(Author): 覃莉
参考文献(References)：
- [1]汪志诚.热力学·统计物理[M].北京:高等教育出版社,1996.
- [2]梁希侠,班士良.统计热力学[M].北京:科学出版社,2008.
- [3]包景东.热力学与统计物理简明教程[M].北京:高等教育出版社,2011.
- [4]JARZYNSKI C.Nonequilibrium equality for free energy differences[J].Phys.Rev.Lett.,1997,78(14):2690-2693.
- [5]覃莉.小系统涨落定理及各态历经行为的研究[D].北京:北京师范大学,2009.QIN Li.Studies on fluctuation theorems and nonergodic behavior of small systems[D].Beijing:Beijing Normal University,2009.(in Chinese)
- [6]BUSTAMANTE C,LIPHARDT J,RITORT F.The nonequilibrium thermodynamics of small systems[J].Phys.Today,2005,58(7):43-48.
- [7]怀小鹏.涨落定理和不可逆性[D].杭州:浙江大学,2012.HUAI Xiaopeng.Fluctuation theorems and irreversibility[D].Hangzhou:Zhejiang University,2012.(in Chinese)
- [8]葛颢.随机过程在非平衡态统计物理和系统生物学建模中的应用[D].北京:北京大学,2008.GE Hao.Applications of stochastic processes into nonequilibrium statistical physics and systems biology[D].Beijing:Peking University,2008.(in Chinese)
- [9]HATANO T,SASA S.Steady-states thermodynamics of Langevin systems[J].Phys.Rev.Lett.,2001,86(16):3463-3466.
- [10]陈天.量子体系的能量操控以及微观器件的研究[D].北京:清华大学,2015.CHEN Tian.Manipulation of thermal flux in quantum systems and study of microscopic Devices[D].Beijing:Tsinghua University,2015.(in Chinese)
- [11]DEFFNER S,SAXENA A.Jarzynski equality in PT-symmetric quantum mechanics[J].Phys.Rev.Lett.,2015,114(15):150601.
- [12]CHERNYAK V Y,CHERTKOV M,JARZYNSKI C.Path-integral analysis of fluctuation theorems for general Langevin processes[J].J.Stat.Mech.,2006,P08001.
- [13]ANDRIEUX D,GASPARD P.Quantum work relations and response theory[J].Phys.Rev.Lett.,2008.100(23):230404.
- [14]SPECK T,SEIFERT U.The Jarzynski relation,fluctuation theorems,and stochastic thermodynamics for non-Markovian processes[J].J.Stat.Mech.-Theory E.,2007,L09002.
- [15]OHKUMA T,OHTA T.Fluctuation theorems for nonlinear generalized Langevin systems[J].J.Stat.Mech.-Theory E.,2007,P10010.
- [16]江惠军.介观统计力学规律与方法的研究[D].合肥:中国科学技术大学,2011.JIANG Huijun.Studies of mechanism and method on mesoscopic statistical mechanics[D].Hefei:University of Science and Technology of China,2011.(in Chinese)
- [17]GONG Z P,QUAN H T.Jarzynski equality,Crooks fluctuation theorem,and the fluctuation theorems of heat for arbitrary initial states[J].Phys.Rev.E,2015,92(1):012131.
- [18]HUMMER G,SZABO A.Free energy reconstruction from nonequilibrium single-molecule pulling experiments[J].Proc.Natl.Acad.Sci.USA,2001,98(7):3658-3661.
- [19]LIPHARDT J,DUMONT S,SMITH S B,et al.Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality[J].Science,296(5574),2002:1832-1835.
- [20]涂展春.小系统的非平衡统计力学与随机热力学[J].物理,2014,43(7):453-459.TU Zhanchun.Nonequilibrium statistical mechanics and stochastic thermodynamics of small systems[J].Physics,2014,43(7):453-459.(in Chinese)
- [21]BLICKLE V,SPECK T,HELDEN L,et al.Thermodynamics of a colloidal particle in a time-dependent nonharmonic potential[J].Phys.Rev.Lett.,2006,96(7):070603.
- [22]JOUBAUD S,GARNIER N B,DOUARCHE F,et al.Experimental study of work fluctuations in a harmonic oscillator[J].C.R.Physigue,2007,8(5-6):518-527.
- [23]AN S M,ZHANG J N,UM M,et al.Experimental test of the quantum Jarzynski equality with a trapped-ion system[J].Nature Phys.,2015,11(2):193-199.