Macrostate equivalence of two gen- eral ensembles and specic relative entropies
Macrostate equivalence of two gen- eral ensembles and specic relative entropies
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两个一般系综和特定相对熵的宏观状态等价
DOI：
10.1103/physreve.94.020101
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发表时间：
2016
影响因子：
2.4
通讯作者：
Takashi Mori
中科院分区：
文献类型：
--
作者：
Tatsuhiko Shirai;Juzar Thingna;Takashi Mori;Sergey Denisov;Peter Hanggi;and Seiji Miyashita;Takashi Mori
系综等效的两个标准，即，宏观状态等价和测度等价。宏观态等价意味着两个系综在遵循大偏差原理的宏观量的测量下是不可区分的，而测量等价意味着这两个态的比相对熵在热力学极限下为零。它表明，测量等价意味着一个宏观状态等价的一般状态对导出一个不等式连接的大偏差率函数的特定的相对Renyi熵。这个结果既适用于量子系统，也适用于经典系统.作为应用，讨论了量子量子化的一个充分条件、宏观变量量子动力学的时间尺度以及量子猝灭中严格不可逆的第二定律。
The two criteria of ensemble equivalence, i.e., macrostate equivalence and measure equivalence, are investigated for a general pair of states. Macrostate equivalence implies the two ensembles are indistinguishable by the measurement of macroscopic quantities obeying the large-deviation principle, and measure equivalence means that the specific relative entropy of these two states vanishes in the thermodynamic limit. It is shown that measure equivalence implies a macrostate equivalence for a general pair of states by deriving an inequality connecting the large-deviation rate functions to the specific relative Renyi entropies. The result is applicable to both quantum and classical systems. As applications, a sufficient condition for thermalization, the time scale of quantum dynamics of macrovariables, and the second law with strict irreversibility in a quantum quench are discussed.