  At stationary environmental conditions, a catalyst's reaction rates may be
restricted by thermodynamic laws, and certain performances can never be
achieved (e.g., catalysts can not change the free energy difference between
reactants and products). However, it has been reported that if environments
change rapidly, catalysts can be driven away from stationary states and exhibit
anomalous performance. We present a general geometric non-equilibrium theory to
describe and explain anomalous catalytic behaviors in rapidly oscillating
environments that exceed the steady-state restrictions. It leads to a universal
design principle of novel catalysts with oscillation-pumped performances. Even
though a catalyst at various environmental conditions cannot be described by a
single free energy landscape, we propose a novel control-conjugate landscape to
encode the reaction rates over a continuous range of control parameters
$\lambda$, which is inspired by the exponential form of the Arrhenius law. The
control-conjugate landscape significantly simplifies the design principle and
makes it applicable to large-amplitude environmental oscillations. The design
principle is demonstrated by two examples, (1) inverting a spontaneous reaction
to synthesize high-free-energy molecules and (2) speeding up reactions without
utilizing low activation barriers. In both examples, catalysts autonomously
harness energy from non-equilibrium environments to enable such
functionalities.
