HMF模型中的非齐次Tsallis分布
Inhomogeneous Tsallis distributions in the HMF model
摘要：
研究了HMF模型中Tsallis泛函在固定质量和能量下的最大化问题。我们给出了这个变分原理的一个热力学和动力学解释。这导致了天体物理学中称为恒星多面体的q分布。我们研究了空间均匀和空间非均匀平衡态之间的相变。我们证明了存在一个特殊的指数q_c=3，它起着分离正则系综中一级和二级相变的正则三临界点的作用，并标志着微正则系综中出现负比热区。我们把我们的结果应用到Antoni & Ruffo [Phys.Rev.E52，2361（1995）]所考虑的情况中，并表明在他们的热量曲线上显示的异常可以通过假设在这个区域中类星体是临界指数q_c=3的多面体而自然地解释。我们定性地证明了多变（Tsallis）分布的发生与紧凑的支持不完全放松和低效率的混合（非遍历性）。本文对HMF模型中的多变分布进行了详尽的研究，并首次对Antoni和Ruffo（1995）在数值上观察到的令人惊讶的结果做出了合理的解释。在我们的分析过程中，我们还报告了一个有趣的情况下，热量曲线呈现微正则第一和第二阶相变。
英文摘要：
We study the maximization of the Tsallis functional at fixed mass and energy in the HMF model. We give a thermodynamical and a dynamical interpretation of this variational principle. This leads to q-distributions known as stellar polytropes in astrophysics. We study phase transitions between spatially homogeneous and spatially inhomogeneous equilibrium states. We show that there exists a particular index q_c=3 playing the role of a canonical tricritical point separating first and second order phase transitions in the canonical ensemble and marking the occurence of a negative specific heat region in the microcanonical ensemble. We apply our results to the situation considered by Antoni & Ruffo [Phys. Rev. E 52, 2361 (1995)] and show that the anomaly displayed on their caloric curve can be explained naturally by assuming that, in this region, the QSSs are polytropes with critical index q_c=3. We qualitatively justify the occurrence of polytropic (Tsallis) distributions with compact support in terms of incomplete relaxation and inefficient mixing (non-ergodicity). Our paper provides an exhaustive study of polytropic distributions in the HMF model and the first plausible explanation of the surprising result observed numerically by Antoni & Ruffo (1995). In the course of our analysis, we also report an interesting situation where the caloric curve presents both microcanonical first and second order phase transitions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
