A Thermodynamic Lower Bound on Sustained Quantum Identity

Fault-tolerant quantum computation relies on continuous error-correcting processes to preserve logical identity over time. While fault-tolerance threshold theorems bound logical error rates per operation, the thermodynamic cost of sustaining quantum identity under ongoing maintenance has not been explicitly isolated. In this work, we show that any fault-tolerant quantum system that preserves logical identity through active error correction must dissipate heat at a rate bounded below by the irreversible information processed during syndrome extraction and reset. As a consequence, at fixed temperature and cooling power, there exists an upper bound on the sustained throughput of fault-tolerant quantum identity, independent of code family, decoding strategy, or physical noise model. The result establishes a fundamental persistence–dissipation constraint arising from irreversible maintenance rather than from quantum dynamics themselves. This work is intentionally descriptive and non-operational, identifying a structural thermodynamic bound without proposing mechanisms, architectures, or control strategies.