量子熵模糊性：乙烯
Quantum Entropic Ambiguities: Ethylene
摘要：
在量子系统中，可以有许多密度矩阵与观测量代数上的状态相关联。对于每个密度矩阵，可以计算其熵。这些一般是不同的。因此，人们达到了一个显着的可能性，即可能有许多熵为一个给定的状态[私人通信从R。Sorkin]。熵的这种不确定性常常可以追溯到一种规范对称性，这种对称性是由底层系统的位形空间的非平凡拓扑特征所产生的。它也可以发生在有限维矩阵模型中。在目前的工作中，我们讨论了这种熵的模糊性及其后果的乙烯分子。这是一个非常简单和众所周知的系统，可以对这些概念进行测试。除了其内在的概念兴趣，这个模型的简单性可以作为一个类似的系统，如彩色单极子和打破颜色对称性的讨论介绍。
英文摘要：
In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are in general different. Therefore one reaches the remarkable possibility that there may be many entropies for a given state [Private communication from R. Sorkin]. This ambiguity in entropy can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. It can also happen in finite-dimensional matrix models. In the present work, we discuss this entropy ambiguity and its consequences for an ethylene molecule. This is a very simple and well-known system where these notions can be put to tests. Besides its intrinsic conceptual interest, the simplicity of this model can serve as an introduction to a similar discussion of systems such as coloured monopoles and the breaking of colour symmetry.
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