Equilibrium and out of equilibrium phase transitions in systems with long range interactions and in 2D flows
Freddy Bouchet, Julien Barré, Antoine Venaille
发表信息：
Dans DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG RANGE INTERACTIONS: Theory and Experiments - DYNAMICS AND THERMODYNAMICS OF SYSTEMS WITH LONG RANGE INTERACTIONS: Theory and Experiments, Italie (2007)
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with many claims, the equilibrium statistical mechanics of such systems is a well understood subject. In this proceeding, we explain briefly the classical approach to equilibrium and non equilibrium statistical mechanics for these systems, starting from first principles. We emphasize recent and new results, mainly a classification of equilibrium phase transitions, new unobserved equilibrium phase transition, and out of equilibrium phase transitions. We briefly discuss what we consider as challenges in this field.
Energy flow and fluctuations in non-equilibrium conformal field theory on star graphs
我们考虑了在星图组态上的共形场论（CFT）中的非平衡量子定态，在图的顶点处具有一个特殊的简单连接条件。这些稳定状态在很长一段时间后出现，这是由于在不同温度下初始热化图的腿，并携带能量流。使用纯粹的Virasoro代数计算，我们评估这些流量的确切的长时间累积量生成函数。我们表明，这个函数满足一般的非平衡波动关系。这将两位作者的结果（J. Phys. A 45：362001，2012; arXiv：1302.3125）扩展到两条腿以上的情况。给出了一种以维拉索罗代数算子为中心而不是以局部域为中心的推导方法，从而给出了另一种正则化方案，从而证实了长时间累积量母函数的有效性和普适性.我们的推导表明，如何通常的维拉索罗代数导致，在大量的，一个连续的指数维拉索罗代数，我们开发的数学原理，这可能是感兴趣的其他非平衡环境以及。最后，我们的研究结果揭示了泊松过程解释的长时间能量转移的CFT。
