Thermodynamic Inductive Synthesis: A Physics-Constrained Framework for Energy-Optimal Logic Generation

The fundamental energetic limit of computation is established by Landauer's Principle, which dictates a lower bound of heat generation for every bit of information erased. While modern Inductive Logic Programming (ILP) has achieved significant success in symbolic rule induction, current frameworks remain thermodynamically blind; they optimise for symbolic accuracy while treating physical energy cost as an externality. In the post-Moore era, we argue that a logically valid program that is thermodynamically unviable is fundamentally incorrect for deployment in energy-constrained sovereign environments. This paper introduces Thermodynamic Inductive Synthesis (TIS), a closed-loop framework that integrates physical entropy production directly into the logic generation process. Presented here is the Fine-Grained Reconfigurable Thermodynamic Substrate (FGRTS), a hardware architecture capable of measuring transient Localised Entropy Production Rate (LEPR) at the gate-cluster level. These measurements serve as a feedback signal for a Gradient-Based Inductive Synthesiser (GBIS), which extends differentiable relaxation techniques to penalise irreversible state changes. We analytically derive that TIS-generated primitives are projected to reduce irreversible entropy production by approximately 40% compared to standard synthesis baselines, theoretically predicting the spontaneous emergence of quasi-adiabatic logic topologies similar to those predicted by conservative logic theory.