Given a closed quantum system, the states that can be reached with a cyclic process are those with the same spectrum as the initial state. Here we prove that, under a very general assumption on the Hamiltonian, the distribution of the mean extractable work is very close to a gaussian with respect to the Haar measure. We derive bounds for both the moments of the distribution of the mean energy of the state and for its characteristic function, showing that the discrepancy with the normal distribution is increasingly suppressed for large dimensions of the system Hilbert space.

中文翻译：

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量子态酉轨道中平均能量的分布

给定一个封闭的量子系统，循环过程可以达到的状态是与初始状态具有相同光谱的状态。在这里我们证明，在对哈密顿量的一个非常一般的假设下，平均可提取功的分布非常接近于哈尔测度的高斯分布。我们推导出状态平均能量分布的矩及其特征函数的界限，表明对于系统希尔伯特空间的大维度，正态分布的差异越来越受到抑制。