熵：任何系统在任何状态下固有的非统计性质
Entropy: An inherent, nonstatistical property of any system in any state
摘要：
熵是我们努力理解和规范我们对一类非常大的自然现象的观察的最重要的概念，然而，它是物理学中最有争议的概念之一。本文回顾了热力学的两种论述，一种是不涉及量子理论，另一种是不涉及统计力学概率的量子力学。在第一部分中，我们证明了熵是任何系统在任何状态下的固有属性，并且它的解析表达式必须符合八个标准。在第二种情况下，我们认识到量子热力学：（i）允许用波函数或非统计密度算符描述量子概率;（ii）需要一个非线性运动方程，它由薛定谔方程限定，但比薛定谔方程更一般，并且它能解释系统状态随时间的可逆和不可逆演化。更一般的量子几率和运动方程都已被定义，热力学三大热力学定律被证明是这个方程的定理。
英文摘要：
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this article, we review two expositions of thermodynamics, one without reference to quantum theory, and the other quantum mechanical without probabilities of statistical mechanics. In the first, we show that entropy is an inherent property of any system in any state, and that its analytical expression must conform to eight criteria. In the second, we recognize that quantum thermodynamics: (i) admits quantum probabilities described either by wave functions or by nonstatistical density operators; and (ii) requires a nonlinear equation of motion that is delimited by but more general than the Schroedinger equation, and that accounts for both reversible and irreversible evolutions of the state of the system in time. Both the more general quantum probabilities, and the equation of motion have been defined, and the three laws of thermodynamics are shown to be theorems of this equation.
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