论文标题
非线性热力学形式主义
Nonlinear thermodynamical formalism
论文作者
论文摘要
我们定义了一种非线性热力学形式主义，该形式主义转化为动力学系统理论广义平均模型的统计力学，从而扩展了鳞翅目和Watbleed对二次病例的研究。 在适当的条件下，我们证明了非线性压力的变异原理，并且表征了非线性平衡度量，并将其与特定的经典平衡度量相关联。 在这种非线性热力学形式主义中，例如，大型系统的模型平均场近似值，出现了几种相变，其中一些相位在线性情况下不可能发生。我们在非线性和线性平衡度量之间使用对应关系，以进一步理解相变（在先前已知的情况下（Curie-Weiss和Potts模型），以及在}新示例（亚稳态相变）中。 最后，我们将一些引入的思想应用于经典的热力学形式主义，证明可以在\ emph {any}零entropy不变性的紧凑型子集中发生冻结相变。
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under suitable conditions, we prove a variational principle for the nonlinear pressure and we characterize the nonlinear equilibrium measures and relate them to specific classical equilibrium measures. In this non-linear thermodynamical formalism, which can, e.g., model mean-field approximation of large systems, several kind of phase transitions appear, some of which cannot happen in the linear case. We use our correspondence between non-linear and linear equilibrium measures to further the understanding of phase transitions, { both in previously known cases (Curie-Weiss and Potts models) and in} new examples (metastable phase transition). Finally, we apply some of the ideas introduced to the classical thermodynamical formalism, proving that freezing phase transitions can occur over \emph{any} zero-entropy invariant compact subset of the phase space.
