  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.
