G\'acs' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Shannon-Gibbs entropies, it requires no prior commitment to macrovariables or 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. After adapting G\'acs' definition to Markov processes, we prove a very general second law of thermodynamics, and discuss its advantages over previous formulations. Finally, taking inspiration from Maxwell's demon, we model an information engine powered by compressible data.

翻译：Gács的粗粒化算法熵借助通用计算，量化了任意给定物理态的信息含量。与玻尔兹曼熵和香农-吉布斯熵不同，该熵无需预先设定宏观变量或概率系综。尽管先前的研究仅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。在将Gács定义适配至马尔可夫过程后，我们证明了一个十分普适的热力学第二定律，并讨论了其相较于此前表述的优势。最后，受麦克斯韦妖启发，我们构建了一个以可压缩数据为驱动的信息引擎模型。