  We determine the QCD equation of state at nonzero temperature in the presence
of an isospin asymmetry between the light quark chemical potentials on the
lattice. Our simulations employ $N_f=2+1$ flavors of dynamical staggered quarks
at physical masses, using three different lattice spacings. The main results
are based on a two-dimensional spline interpolation of the isospin density,
from which all relevant quantities can be obtained analytically. In particular,
we present results for the pressure, the interaction measure, the energy and
entropy densities, as well as the speed of sound. Remarkably, the latter is
found to exceed its ideal gas limit deep in the pion condensed phase, the first
account of the violation of this limit in first principles QCD. Finally, we
also compute the phase diagram in the temperature -- isospin density plane for
the first time. The data for all observables will be useful for the
benchmarking of effective theories and low-energy models of QCD and are
provided in ancillary files for simple reuse.
