The Entropic Time Constraint: An Operational Bound on Information Processing Speed

We derive an operationally defined lower bound on the physical time \( \Delta t \)required to execute any information-processing task, based on the total entropy produced \( \Delta\Sigma \). The central result, \( \Delta t \geq \tau_{\Sigma} \Delta\Sigma \), introduces the Process-Dependent Dissipation Timescale \( \tau_{\Sigma} \equiv 1/\langle \dot{\Sigma} \rangle_{\text{max}} \), which quantifies the maximum achievable entropy production rate for a given physical platform. We derive \( \tau_{\Sigma} \) from microscopic system-bath models and validate our framework against experimental data from superconducting qubit platforms. Crucially, we obtain a Measurement Entropic Time Bound:\( \Delta t_{\text{meas}} \geq \tau_{\Sigma} k_{\text{B}}[H(P) - S(\rho)] \), relating measurement time to information gained. Comparison with IBM and Google quantum processors shows agreement within experimental uncertainties. This framework provides a thermodynamic interpretation of quantum advantage as reduced entropy production per logical inference and suggests concrete optimization strategies for quantum hardware design.