The Thermodynamic Cost of Neural Computation: From Landauer’s Bound to the Energetic Gap of Artificial Intelligence

Landauer’s principle establishes a thermodynamic lower bound for physical processes that reduce the logical entropy of information-bearing degrees of freedom, but it does not assign a universal energy cost to every floating-point operation, multiply–accumulate instruction, or transistor transition. This review develops a hierarchical framework for locating energy costs in neural computation while distinguishing three quantities that are frequently conflated: process-specific thermodynamic lower bounds, Landauer-normalized reference ratios, and measured or modelled operational energy. The analysis synthesizes results from stochastic thermodynamics, finite-time and quantum Landauer theory, thermodynamic control, mismatch cost, device physics, computer architecture, and full-stack AI serving. The resulting hierarchy separates logical entropy reduction, finite-time corrections, quantum and strong-coupling effects, control costs, distribution-dependent mismatch, architectural and data-movement costs, and facility overhead. The literature supports rigorous bounds for specified physical processes, but not a universal additive decomposition of the energy consumed by a large-language-model query. An operational accounting analysis shows how accelerator throughput, utilization, host power, sequence length, memory traffic, and facility overhead determine query-level energy. Published full-stack studies place representative text-prompt energies in the sub-watt-hour range while revealing substantial variation across models and serving conditions. Contemporary dissipation is therefore dominated by implementation and systems choices long before fundamental erasure bounds become active constraints. The framework provides a consistent basis for evaluating emerging computing paradigms and designing energy-aware AI benchmarks.