  In this short review article, we present recent progress in quantum
thermodynamics in the framework with a correlated catalyst. We examine two key
properties of thermal operations, the Gibbs preserving property and the
covariant property. The state convertibility of a Gibbs preserving operation is
fully characterized by the second law of thermodynamics with the nonequilibrium
free energy. The state convertibility of a covariant operation is shown to be
free as long as an initial state has finite coherence. We finally show that
these two findings can be combined in the enhanced thermal operation (covariant
Gibbs-preserving operation).
