论文标题
布朗粒子在非固定场中的正则玻尔兹曼·吉布斯统计
Regularized Boltzmann-Gibbs statistics for a Brownian particle in a non-confining field
论文作者
论文摘要
我们认为一个过度阻尼的棕色粒子具有渐近平坦的电位，其原点周围具有深度$ u_0 $的陷阱。与陷阱深度相比，温度很小（$ξ= k_b t/u_0 \ ll 1 $）时，存在一系列时间表，这些时间表实际上可观察到实际上保持恒定。这个范围可能很长，是Arrhenius因子$ {\ rm e}^{1/ξ} $的顺序。对于这些准平衡状态，通常的Boltzmann-Gibbs食谱无效，因为由于长距离电势的平稳性，分区函数有分歧。但是，我们表明标准的玻尔兹曼 - 吉布斯（BG）统计框架和热力学关系仍然可以通过适当的正则化应用。这可能是在表征大量系统的非固定潜在领域中分析亚稳定性的宝贵工具。
We consider an overdamped Brownian particle subject to an asymptotically flat potential with a trap of depth $U_0$ around the origin. When the temperature is small compared to the trap depth ($ξ=k_B T/U_0 \ll 1$), there exists a range of timescales over which physical observables remain practically constant. This range can be very long, of the order of the Arrhenius factor ${\rm e}^{1/ξ}$. For these quasi-equilibrium states, the usual Boltzmann-Gibbs recipe does not work, since the partition function is divergent due to the flatness of the potential at long distances. However, we show that the standard Boltzmann-Gibbs (BG) statistical framework and thermodynamic relations can still be applied through proper regularization. This can be a valuable tool for the analysis of metastability in the non-confining potential fields that characterize a vast number of systems.
