Finite-Time Thermodynamics of Battery Discharging: Power-Efficiency Trade-Off and Optimization

Battery discharging is governed by a fundamental trade-off between output power and energy conversion efficiency due to internal dissipation. In this paper, we demonstrate that such a trade-off universally yields a parabolic envelope $P\propto\eta(1-\eta)$. The efficiency at maximum power is exactly one half, mirroring the well-known half-Carnot limit in finite-time thermodynamics. To extend this bound into practical operational rules, we formulate a multistage constant-current discharging (MSCD) schedule subject to simultaneous real-time load demands and a global discharging deadline. Analytical resolution via the Karush--Kuhn--Tucker conditions reveals a remarkably compact optimal policy: $I_{i}^{\star}=\max(I_{i}^{-},I_{0})$. Under this rule, stages limited by external demand run exactly at their minimum required currents, while all remaining stages are elevated to a uniform baseline $I_{0}$ fixed by the deadline constraint. By tracing the dissipation--time Pareto front, we quantify how internal resistance shifts the operational boundaries and sharpens the trade-off corner. This analysis establishes a rigorous thermodynamic baseline for the scheduling layer of battery management systems, offering natural extensions to nonlinear models incorporating temperature and state-of-charge dependencies.