Beyond Efficiency: A Unified Survival–Conversion Law for Useful Energy in Physical and Information Systems

Despite sustained advances in semiconductor fabrication, transistor miniaturization, and device-level energy efficiency, modern data centers consistently convert only 0.5–2% of supplied electrical energy into useful computational work. This striking discrepancy between component-level efficiency and system-level output has persisted across multiple technology generations and is observed globally in hyperscale cloud infrastructure, high-performance computing clusters, and AI training facilities. Conventional explanations attribute this outcome to engineering shortcomings such as inefficient cooling, poor workload utilization, or legacy infrastructure overhead. However, these explanations fail to account for the universality, stability, and scale-independence of the observed limit. Even in state-of-the-art facilities employing advanced cooling, near-optimal power usage effectiveness (PUE), and highly efficient processors, the fraction of input energy contributing directly to information processing remains fundamentally constrained. Here, we demonstrate that this low computational energy fraction is not an engineering failure, but an unavoidable physical consequence of energy survival losses and internal conversion saturation, governed by thermodynamics and information theory. Using the Unified Energy Survival–Conversion Law, Euseful=Ein⋅Ψ⋅Cint with the survival factor defined as Ψ=AE/TE+ε we show that large-scale computing infrastructure operates in a conversion-limited regime, where internal information throughput Cint, rather than component efficiency or energy supply, imposes the dominant upper bound on useful output. This formulation resolves the long-standing paradox of why increasingly efficient processors fail to yield proportional reductions in data-center energy consumption and establishes hard thermodynamic limits on the scalability of computation. Please check the attachment for details