  We establish a rigorous connection between fundamental resource theories at
the quantum scale. Correlations and entanglement constitute indispensable
resources for numerous quantum information tasks. However, their establishment
comes at the cost of energy, the resource of thermodynamics, and is limited by
the initial entropy. Here, the optimal conversion of energy into correlations
is investigated. Assuming the presence of a thermal bath, we establish general
bounds for arbitrary systems and construct a protocol saturating them. The
amount of correlations, quantified by the mutual information, can increase at
most linearly with the available energy, and we determine where the linear
regime breaks down. We further consider the generation of genuine quantum
correlations, focusing on the fundamental constituents of our universe:
fermions and bosons. For fermionic modes, we find the optimal entangling
protocol. For bosonic modes, we show that while Gaussian operations can be
outperformed in creating entanglement, their performance is optimal for high
energies.
