Cercignani猜想对Smoluchowski凝聚方程成立
Cercignani conjecture is true for Smoluchowski coagulation equation
摘要：
本文从统计物理学的角度提出了smoluchowski混凝方程的信息熵。根据最大熵原理和矩约束，在平衡状态下，归一化的粒度分布是对数正态分布。将粒度分布中的参数确定为简单常数，结果表明，自保持假设中代数平均体积为单位的假设是合理的。在现有信息熵定义的基础上，对Smoluchowski凝聚方程，Cercignani猜想自然成立。Cercignani猜想不仅对Boltzmann方程成立，而且对任何两体碰撞系统都成立，这将有助于理解布朗运动和分子运动学理论，如耗散系统的稳定性和收敛于热力学平衡的数学理论.
英文摘要：
In the present study, the information entropy for smoluchowski coagulation equation is proposed based on the statistical physics. and the normalized particle size distribution is a log-normal function at equilibrium from the principle of maximum entropy and moment constraint. the parameters in the particle size distribution are determined as simple constants, the result reveals that the assumption that algebraic mean volume be unit in self-preserving hypothesis is reasonable. based on the present definition of the information entropy, the cercignani conjecture holds naturally for smoluchowski coagulation equation. Together with the fact that the conjecture is also true for Boltzmann equation, cercignani conjecture holds for any two-body collision systems, which will benefit the understanding of Brownian motion and molecule kinematic theory, such as the stability of the dissipative system, and the mathematical theory of convergence to thermodynamic equilibrium.
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