负热力学温度的统计解释和负温度热力学  

Statistical Explanation of the Negative Thermodynamic Temperature and the Thermodynamics at Negative Temperature

作　　者：包科达 

机构地区：[1]北京大学,物理学院,北京

出　　处：《应用物理》2020年第3期205-215,共11页Applied Physics

摘　　要：文章以二能级的核自旋系统为例,对负热力学温度的基本概念、研究方向以及其研究的现状,作了较为详细的讨论和介绍。首先,文中从统计力学的角度,给出了二能级核自旋分布的严格数学解;在此基础上的研究表明,为确定系统热力学性质例如玻耳兹曼熵,重要的是系统的最概然分布。研究还表明,系统的负温度并不比绝对零度冷,而比无限大的正温度状态更热。其次,文章指出除能量必须有限条件外,系统能处于热平衡的负温度状态,还必需满足的一个重要条件是: ,其中 是核自旋系统与核之间经过相互作用,达到热平衡所需的弛豫时间;而 是系统与整个晶体通过相互作用,发生能量传递而建立热平衡所需的特征时间。再次,本文在熵增加原理基础上,发展了负温度热力学;研究确认,在负温度系统中,第二类永动机是可以制成的;热力学第二定律的开耳文表述必须改变。在负温系统中功是不能自发地转化为热的,而热却能自发地转化为功,而不产生其它影响。最后,在考虑到可能存在的负温度状态后,热力学第三定律的不可达原理应充实扩展为:通过有限数目手续的操作,既不可能使凝聚系冷却到正绝对零度(+0 K),也不可能使系统加热到负绝对零度(?0 K)。Using a nuclear spin system of two energy levels, as an example, a detailed introduction and dis-cussion to the conceptions, research methods and current status of negative thermodynamic temperature is presented. At first, from statistical mechanics point of view, an exact solution of the nuclear spin distributions is developed. Consequently, it is showed that for determining the thermodynamics properties of spin systems, for example the Bolzmann entropy, a most probable distribution is important. Negative temperatures are not cooler than positive absolute zero, but instead hotter than infinite positive temperature. Secondary, it is emphasized that except the system energy should be finite, another important condition under which negative temperatures can occur is , where is the relaxation time for establishing the thermal equilibrium between the nuclear and nuclear spin system by their interaction, and is the characteristic time for establishing the thermal equilibrium between the nuclear and LIF lattice by their interaction and energy exchange. Thirdly, based upon the principle of entropy increase, the thermodynamics at negative temperatures is developed. It is shown that at negative temperatures, the perpetual motion machine of second kind may be constructed. The Kelvin formulation of the second law of thermodynamics must be altered. At the negative temperatures work cannot be spontaneously transformed into the heat, but heat can be extracted from a negative temperature reservoir with no other influences than the performance of an equivalent amount of work. Finally, on account for the fact that systems can be existed in the negative thermodynamic temperature states, the principle of the unattainability statement of the third law of thermodynamics must be expanded as: by finite series of processes not only is the positive absolute zero no attainable, but also is the negative absolute zero no attainable.

关 键 词：负热力学温度 二能级核自旋系统 最概然分布 负温度热力学 

分 类 号：O41[理学—理论物理]