吉布斯均衡收敛-揭开神秘面纱
Convergence to Gibbs equilibrium - unveiling the mystery
摘要：
本文考虑具有二次相互作用势和$N<\infty$自由度的一般哈密顿系统，其中只有$m$与外界接触，即受到阻尼和随机平稳外力的作用。我们表明，作为$t\to\infty$，已经为$m=1$，唯一的极限分布存在于几乎所有的相互作用。此外，如果外力是白噪声，则它是吉布斯，但对于具有平滑轨迹的高斯过程，通常不是吉布斯。这一结论在热力学极限$N\to\infty$下也成立。
英文摘要：
We consider general hamiltonian systems with quadratic interaction potential and $N<\infty$ degrees of freedom, only $m$ of which have contact with external world, that is subjected to damping and random stationary external forces. We show that, as $t\to\infty$, already for $m=1$, the unique limiting distribution exists for almost all interactions. Moreover, it is Gibbs if the external force is the white noise, but typically not Gibbs for gaussian processes with smooth trajectories. This conclusion survives also in the thermodynamic limit $N\to\infty$.
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