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, rendering it applicable to settings arbitrarily far from equilibrium. For Markovian coarse-grainings, we prove a number of algorithmic fluctuation inequalities. The most important of these is a very general formulation of the second law of thermodynamics. In the presence of a heat and work reservoir, it implies algorithmic versions of Jarzynski's equality and Landauer's principle. Finally, to demonstrate how a deficiency of algorithmic entropy can be used as a resource, we model an information engine powered by compressible strings.

翻译：Gács的粗粒化算法熵利用通用计算来量化任何给定物理状态的信息含量。与玻尔兹曼熵和香农-吉布斯熵不同，它无需预先设定宏观变量或概率系综，因此适用于任意远离平衡态的情形。针对马尔可夫粗粒化过程，我们证明了一系列算法涨落不等式，其中最重要的结论是热力学第二定律的一种极普适形式。当存在热功库时，该定律推导出Jarzynski等式和朗道尔原理的算法版本。最后，为展示算法熵的缺失可作为资源加以利用，我们构建了一个由可压缩字符串驱动的信息引擎模型。