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 sets a lower bound on heat generation for every bit of information erased. Modern Inductive Logic Programming (ILP) has achieved significant success in symbolic rule induction, low-power electronic design automation has long optimised circuits for switching energy, and evolvable hardware has used run-time power measurements as an objective. The combination studied here is gradient-based synthesis of Boolean netlists from continuous structural parameters, using scalar dissipation readings from sampled discrete netlists in the objective.

This paper introduces Thermodynamic Inductive Synthesis (TIS), a proposed closed-loop framework that integrates in situ dissipation measurement directly into the logic generation process. We describe the Fine-Grained Reconfigurable Thermodynamic Substrate (FGRTS), a hardware architecture for measuring transient dissipation at the gate-cluster level, and the Gradient-Based Inductive Synthesiser (GBIS), which extends differentiable relaxation techniques to penalise measured dissipation. We derive the logical irreversibility floor for two benchmark primitives from first principles: a 4-bit magnitude comparator erases 6.73 bits per operation (1.93 × 10⁻²⁰ J at 300 K) and a 4-bit parity checker erases 3.00 bits (8.61 × 10⁻²¹ J). Under stated and clearly flagged assumptions, we project a composite dissipation reduction of approximately 32% relative to standard-cell synthesis; this projection is not tested here.

We then test the proposed loop in a software study whose design was fixed before the main runs, with an analytical switching model in place of the substrate. From random initialisation, the relaxed synthesiser found a correct netlist in 2 of 20 runs on the parity checker and in none of 20 on the comparator. From correct starting netlists, energy readings used through a REINFORCE estimator with a correctness gate removed an inserted, removable inverter pair in every run, also with 1% sensor noise; SPSA, and a control whose readings carry no energy information, did not. On netlists from a Yosys and ABC flow, the gradient-based loop found no improvement beyond what the semantic loss alone found, whereas a simple evolution strategy without sensor noise found a 2.5% reduction on the comparator for uniform random inputs, which did not carry over to structured inputs. No hardware has been built, and the gradient estimator for a physical substrate remains the principal open problem (Section 4.3).

Version 3 adds the software study (Section 6). TIS_v3_code_and_data.zip contains the study specification, every amendment, the code, and every tuning and main-run record. Version 2 was the framework and architectural proposal without experimental or simulated results.