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相对玻尔兹曼熵、热力学强度变量涨落的演化方程以及热力学第零定律的统计力学表示。

Relative Boltzmann entropy, evolution equations for fluctuations of thermodynamic intensive variables, and a statistical mechanical representation of the zeroth law of thermodynamics.

作者信息

Chan Eu Byung

机构信息

Department of Chemistry, McGill University, 801 Sherbrooke St. West, Montreal, Quebec H3A 2K6, Canada.

出版信息

J Chem Phys. 2006 Aug 14;125(6):64110. doi: 10.1063/1.2208360.

DOI:10.1063/1.2208360
PMID:16942276
Abstract

Generalized thermodynamics or extended irreversible thermodynamics presumes the existence of thermodynamic intensive variables (e.g., temperature, pressure, chemical potentials, generalized potentials) even if the system is removed from equilibrium. It is necessary to properly understand the nature of such intensive variables and, in particular, of their fluctuations, that is, their deviations from those defined in the extended irreversible thermodynamic sense. The meaning of temperature is examined by means of a kinetic theory of macroscopic irreversible processes to assess the validity of the generalized (or extended) thermodynamic method applied to nonequilibrium phenomena. The Boltzmann equation is used for the purpose. Since the relative Boltzmann entropy has been known to be intimately related to the evolution of the aforementioned fluctuations in the intensive thermodynamic variables, we derive the evolution equations for such fluctuations of intensive variables to lay the foundation for investigating the physical implications and evolution of the relative Boltzmann entropy, so that the range of validity of the thermodynamic theory of irreversible processes can be elucidated. Within the framework of this work, we examine a special case of the evolution equations for the aforementioned fluctuations of intensive variables, which also facilitate investigation of the molecular theory meaning of the zeroth law of thermodynamics. We derive an evolution equation describing the relaxation of temperature fluctuations from its local value and present a formula for the temperature relaxation time.

摘要

广义热力学或扩展不可逆热力学假定即使系统偏离平衡态,热力学强度变量(例如温度、压力、化学势、广义势)依然存在。有必要正确理解此类强度变量的本质,尤其是它们的涨落,即它们相对于扩展不可逆热力学意义下所定义的值的偏差。通过宏观不可逆过程的动力学理论来考察温度的意义,以评估应用于非平衡现象的广义(或扩展)热力学方法的有效性。为此使用了玻尔兹曼方程。由于已知相对玻尔兹曼熵与上述强度热力学变量涨落的演化密切相关,我们推导强度变量此类涨落的演化方程,为研究相对玻尔兹曼熵的物理意义和演化奠定基础,从而阐明不可逆过程热力学理论的有效性范围。在这项工作的框架内,我们考察强度变量上述涨落演化方程的一个特殊情况,这也有助于研究热力学第零定律的分子理论意义。我们推导了一个描述温度涨落从其局部值弛豫的演化方程,并给出了温度弛豫时间的公式。

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