Deutsch J M, Li Haibin, Sharma Auditya
Department of Physics, University of California, Santa Cruz, California 95064, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):042135. doi: 10.1103/PhysRevE.87.042135. Epub 2013 Apr 30.
The quantum entropy is usually defined using von Neumann's formula, which measures lack of information and vanishes for pure states. In contrast, we obtain a formula for the entropy of a pure state as it is measured from thermodynamic experiments, solely from the self-entanglement of the wave function, and find strong numerical evidence that the two are in agreement for nonintegrable systems, both for energy eigenstates and for states that are obtained at long times under the evolution of more general initial conditions. This is an extension of Boltzmann's hypothesis for classical systems, relating microscopic motion to thermodynamics.
量子熵通常是用冯·诺依曼公式来定义的，该公式衡量信息的缺失，对于纯态为零。相比之下，我们从热力学实验测量的角度得到了一个关于纯态熵的公式，它仅来自波函数的自纠缠，并发现了强有力的数值证据，表明对于不可积系统，无论是能量本征态还是在更一般初始条件演化下长时间得到的态，这两者是一致的。这是玻尔兹曼关于经典系统假设的一种扩展，将微观运动与热力学联系起来。
