能量-温度涨落关系的几何方面和联系
Geometrical aspects and connections of the energy-temperature fluctuation relation
摘要：
最近，我们导出了热容$C$和能量涨落之间的正则涨落关系$k_{B}C=β^{2}< δU^{2} >$的推广，它可以解释具有负热容$C<0$的宏观态的存在.在这项工作中，我们提出了一个全景的直接影响和连接的统计力学的其他发展，如正则蒙特卡罗方法的扩展，波动理论的几何公式和吉布斯正则系综的几何扩展，最近在文献中提出的相关性的波动定理。
英文摘要：
Recently, we have derived a generalization of the known canonical fluctuation relation $k_{B}C=β^{2}< δU^{2} >$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. In this work, we presented a panoramic overview of direct implications and connections of this fluctuation theorem with other developments of statistical mechanics, such as the extension of canonical Monte Carlo methods, the geometric formulations of fluctuation theory and the relevance of a geometric extension of the Gibbs canonical ensemble that has been recently proposed in the literature.
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