摘要翻译：
讨论了机械系统在不同温度下与两个确定性恒温器接触时的瞬态和稳态涨落关系。该系统是一个修正的洛伦兹气体，固定散射体与粒子气体进行能量交换，恒温器由两个安装在系统边界的Nos\'e-Hoover恒温器模拟。瞬态涨落关系只适用于初始系综的精确选择，在任何时候都得到了验证，正如所期望的那样。如果考虑不同的初始系综，则需要比介观尺度更长的时间来解决局部平衡。当[D.J.Searles,{\em et al.},J.Stat.Phys.128，1337(2007)]中关于稳态涨落关系有效性的条件得到验证时，这说明了瞬态涨落关系如何渐近地导致稳态关系。对于相空间收缩率$\ZL$和耗散函数$\ZW$的定态涨落，在较短的平均时间下也发现了类似的弛豫区。对于大于介观时间尺度的次数，该量$\ZW$满足涨落关系，具有较好的精度；在这样的时间之后，数量$\zl$似乎开始单调收敛。这与$\zw$和$\zl$的总时间导数不同，以及$\zl$的概率分布函数的尾部是高斯的事实是一致的。
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英文标题：
《On the Fluctuation Relation for Nose-Hoover Boundary Thermostated
  Systems》
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作者：
Carlos Mejia-Monasterio, Lamberto Rondoni
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modelled by two Nos\'e-Hoover thermostats applied at the boundaries of the system. The transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state relation when, as explicitly checked in our systems, the condition found in [D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate $\zL$ and of the dissipation function $\zW$, a similar relaxation regime at shorter averaging times is found. The quantity $\zW$ satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the quantity $\zL$ appears to begin a monotonic convergence after such times. This is consistent with the fact that $\zW$ and $\zL$ differ by a total time derivative, and that the tails of the probability distribution function of $\zL$ are Gaussian.
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PDF链接：
https://arxiv.org/pdf/710.3673