Thermodynamics of Quantum Reservoir Computing

Quantum reservoir computing provides a framework for processing complex temporal data, yet its fundamental computational and energetic limits remain unresolved. Here, we establish a non-equilibrium thermodynamic framework that links the macroscopic predictive performance of driven open quantum systems to their microscopic energetic costs. By mapping the Holevo capacities onto the Bogoliubov-Kubo-Mori geometric manifold, we analytically prove that the computational peak within the quantum critical region originates from a strict spectral resonance: the closing of the energy gap forces the reservoir's transition frequencies to align with the chaotic drive. To evaluate the associated thermodynamic costs, we introduce quantum informational dissipation to quantify the non-predictive historical data structurally retained by the reservoir, deriving a generalized Landauer bound for continuous temporal processing. This reveals a fundamental thermodynamic trade-off: the critical resonance that unlocks optimal predictive capacity inherently maximizes informational dissipation and the irreversible work required for environmental erasure. Furthermore, coherence decomposition demonstrates that dynamic quantum coherences strictly amplify predictive capacity without demanding additional mechanical work. These findings establish the ultimate energetic limits of quantum learning devices, providing theoretical principles for designing energy-efficient quantum neuromorphic hardware.