  Quantum coherence allows for reduced-memory simulators of classical
processes. Using recent results in single-shot quantum thermodynamics, we
derive a minimal work cost rate for quantum simulators that is quasistatically
attainable in the limit of asymptotically-infinite parallel simulation.
Comparing this cost with the classical regime reveals that quantizing classical
simulators not only results in memory compression but also in reduced
dissipation. We explore this advantage across a suite of representative
examples.
