Sotoudeh Zahra
Department of Engineering, California State Polytechnic University, Pomona, CA 91768, USA.
Entropy (Basel). 2019 May 26;21(5):536. doi: 10.3390/e21050536.
In this paper, we examine Khinchin's entropy for two weakly nonlinear systems of oscillators. We study a system of coupled Duffing oscillators and a set of Henon-Heiles oscillators. It is shown that the general method of deriving the Khinchin's entropy for linear systems can be modified to account for weak nonlinearities. Nonlinearities are modeled as nonlinear springs. To calculate the Khinchin's entropy, one needs to obtain an analytical expression of the system's phase volume. We use a perturbation method to do so, and verify the results against the numerical calculation of the phase volume. It is shown that such an approach is valid for weakly nonlinear systems. In an extension of the author's previous work for linear systems, a mixing entropy is defined for these two oscillators. The mixing entropy is the result of the generation of entropy when two systems are combined to create a complex system. It is illustrated that mixing entropy is always non-negative. The mixing entropy provides insight into the energy behavior of each system. The limitation of statistical energy analysis motivates this study. Using the thermodynamic relationship of temperature and entropy, and Khinchin's entropy, one can define a vibrational temperature. Vibrational temperature can be used to derive the power flow proportionality, which is the backbone of the statistical energy analysis. Although this paper is motivated by statistical energy analysis application, it is not devoted to the statistical energy analysis of nonlinear systems.
在本文中，我们研究了两个弱非线性振子系统的欣钦熵。我们考察了一个耦合杜芬振子系统和一组亨农 - 海尔斯振子。结果表明，推导线性系统欣钦熵的一般方法可以进行修改以考虑弱非线性。非线性被建模为非线性弹簧。为了计算欣钦熵，需要得到系统相体积的解析表达式。我们使用微扰方法来做到这一点，并将结果与相体积的数值计算进行验证。结果表明，这种方法对弱非线性系统是有效的。在作者之前关于线性系统工作的扩展中，为这两个振子定义了混合熵。混合熵是两个系统组合形成一个复杂系统时熵产生的结果。结果表明混合熵总是非负的。混合熵为每个系统的能量行为提供了见解。统计能量分析的局限性推动了这项研究。利用温度和熵的热力学关系以及欣钦熵，可以定义一个振动温度。振动温度可用于推导功率流比例关系，这是统计能量分析的核心。尽管本文的动机是统计能量分析应用，但它并不致力于非线性系统的统计能量分析。
