G\'acs' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given state. Unlike the Boltzmann and Shannon-Gibbs entropies, it requires no prior commitment to a partition of phase space or to probabilistic ensembles. Whereas earlier work had made loose connections between the entropy of thermodynamic systems and information-processing systems, the algorithmic entropy formally unifies them both. For a close variant of G\'acs' definition, we prove a very general second law of thermodynamics, and discuss its advantages over previous formulations. Our law is a general property of Markov processes, which can be derived as coarse-grainings of certain time-reversible dynamical systems. Finally, taking inspiration from Maxwell's demon, we model an information engine powered by compressible data.

翻译：Gács的粗粒化算法熵利用通用计算来量化任意给定状态的信息含量。与玻尔兹曼熵和香农-吉布斯熵不同，它无需预先对相空间进行划分或引入概率系综。尽管先前的研究已在热力学系统与信息处理系统的熵之间建立了松散联系，但算法熵在形式上统一了两者。针对Gács定义的近似变体，我们证明了一个极具普适性的热力学第二定律，并讨论了其相较于先前表述的优势。该定律是马尔可夫过程的一个普适性质，可推导为某些时间可逆动力学系统的粗粒化结果。最后，受麦克斯韦妖的启发，我们构建了一个由可压缩数据驱动的信息引擎模型。