我们表明，在弱限制保守力领域，扩散型（Smoluchowski）过程的一个子类，承认一个家庭的“重尾”非高斯平衡概率密度函数（PDF），没有或有限数量的时刻。这些pdf，在标准的吉布斯-玻尔兹曼形式，也可以直接从极值原理推导出来，设置香农熵的约束下，力势的平均值已事先规定。这迫使相应的拉格朗日乘子扮演逆温度的角色。势的弱约束性质表现在一个物理特性上，即在有界温度区间$0\leq T < T_{max} =2ε_0/k_B$内，只有\rm才能接近热平衡，其中$ε_0$设定了一个能量标度.对于$T \geq T_{max}$，不存在平衡pdf。
英文摘要：
We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of "heavy-tailed" non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number of moments. These pdfs, in the standard Gibbs-Boltzmann form, can be also inferred directly from an extremum principle, set for Shannon entropy under a constraint that the mean value of the force potential has been a priori prescribed. That enforces the corresponding Lagrange multiplier to play the role of inverse temperature. Weak confining properties of the potentials are manifested in a thermodynamical peculiarity that thermal equilibria can be approached \it only \rm in a bounded temperature interval $0\leq T < T_{max} =2ε_0/k_B$, where $ε_0$ sets an energy scale. For $T \geq T_{max}$ no equilibrium pdf exists.
Full macroscopic thermalization and the formation of Schrödinger's cats by unitary time evolution in the weakly perturbed Ising model - Applications of the Roos-Sugimoto-Teufel-Tumulka-Vogel theory
Macroscopic thermalization by unitary time evolution in the weakly perturbed two-dimensional Ising model --- An application of the Roos-Sugimoto-Teufel-Tumulka-Vogel theory
Department of Physics, Gakushuin University（学习院大学物理系）
University of Heidelberg（海德堡大学）；Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Pontificia Universidad Católica de Valparaíso（瓦尔帕莱索天主教 Pontificia 大学）；University of Ljubljana（卢布尔雅那大学）
