序列复杂度和工作抽取
Sequence complexity and work extraction
摘要：
我们考虑一个简化版本的可解模型由曼达尔和Jarzynski，建设性地展示了工作提取和增加的信息库，这是在与物理系统的香农熵之间的相互作用。我们扩展曼达尔和Jarzynski的主要研究结果在几个方向：首先，我们允许序列的相关位，而不仅仅是独立的位。其次，至少对于二进制信息的情况下，我们表明，事实上，香农熵是唯一的信息，必须增加，以提取工作的复杂性的措施。提取的工作也可以在衡量复杂性的其他数量的增加方面上有上限，比如从过去的比特中预测未来比特。第三，我们提供了对非二进制信息的情况的扩展（即，更大的字母表），最后，我们将范围扩展到输入位（在交互之前）形成单个序列而不是随机序列的情况。在这种情况下，相互作用之前的熵可以被输入序列的Lempel-Ziv（LZ）复杂度所取代，这一事实不仅在信息论中，而且在物理学中，都产生了LZ复杂度的熵意义。
英文摘要：
We consider a simplified version of a solvable model by Mandal and Jarzynski, which constructively demonstrates the interplay between work extraction and the increase of the Shannon entropy of an information reservoir which is in contact with the physical system. We extend Mandal and Jarzynski's main findings in several directions: First, we allow sequences of correlated bits rather than just independent bits. Secondly, at least for the case of binary information, we show that, in fact, the Shannon entropy is only one measure of complexity of the information that must increase in order for work to be extracted. The extracted work can also be upper bounded in terms of the increase in other quantities that measure complexity, like the predictability of future bits from past ones. Third, we provide an extension to the case of non-binary information (i.e., a larger alphabet), and finally, we extend the scope to the case where the incoming bits (before the interaction) form an individual sequence, rather than a random one. In this case, the entropy before the interaction can be replaced by the Lempel-Ziv (LZ) complexity of the incoming sequence, a fact that gives rise to an entropic meaning of the LZ complexity, not only in information theory, but also in physics.
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