The Finite-Time Exergy Limit of Computation: Reconciling Landauer’s Principle with the Speed-Efficiency Paradox

Abstract

Modern computing hardware operates far from thermodynamic equilibrium, yet the fundamental energy limits of computation are still assessed using the quasistatic Landauer bound, which assumes infinitely slow, reversible operations. Here, we develop a finite-time exergy framework that unifies Landauer's principle with the Gouy–Stodola theorem and linear non-equilibrium thermodynamics to quantify the continuous generation of anergy—the irreversibly degraded fraction of energy—in realistic computing systems. By partitioning the hardware topology into three thermodynamic zones and applying the Onsager formalism to the microscopic substrate, we derive a master equation that decouples the informational, dynamic, and static contributions to computational dissipation as explicit functions of the finite operation time . We prove that the competition between dynamic transport friction () and static leakage () produces a unique thermodynamic optimum , and that the non-linear thermal-leakage feedback generates a saddle-node bifurcation defining the absolute physical speed limit of any dissipative substrate. Applying the framework to a projected 2026 sub-2 nm 3D-IC tensor core and analog ReRAM crossbars, we show that for this specific architecture, the optimal clock frequency converges to 2.36 GHz under realistic thermal constraints. Furthermore, its absolute bifurcation limit at 16.1 GHz is fundamentally coupled to the Landauer informational cost. Our results establish that post-Moore scaling must prioritise macroscopic exergy minimisation over raw frequency scaling.