ESDM–SMTJ: An Entropic Semantic Dynamics Model for Classical Probabilistic Hardware with Superparamagnetic Tunnel Junctions

We introduce ESDM–SMTJ, an Entropic Semantic Dynamics Model implemented on clas- sical probabilistic hardware based on superparamagnetic tunnel junctions (SMTJs). The model represents the internal state of a symbolic or cognitive system as a trajectory Σ(τ ) in a layered state space, with τ ∈ [0, 1] interpreted as an internal computation time from initial query to final answer. Each expression e (for example 2 + 2 =?) induces a program-specific dynamics U τ e that iteratively updates Σ(τ ). Ambiguous operators such as “+” are treated as multi-modal : every occurrence admits a finite family of semantic modes i, and an entropic gate scores each mode by the predicted reduction ∆H(k) i of the output entropy if that mode is selected at position k. These scores are mapped to effective energy levels E(k) i = E0 − κ∆H(k) i in a local SMTJ p-bit block, whose Boltzmann statistics implement a softmax distribution over modes at the hardware level. The resulting dynamics exhibits rumination (high-entropy plateaus), insight-like transi- tions (sharp entropy drops) and stabilization in low-entropy attractors, together with a natural notion of semantic commit at an internal time τc < 1 and a blind reveal of the output token via SMTJ readout at τf ≈ 1. We illustrate how simple arithmetical judgements—including rare anomalies such as 2 + 2 → 5 under mis-tuned parameters—can be expressed in this frame- work, and we outline a quantum extension in which semantic modes become basis states of a Hamiltonian with complex amplitudes instead of classical probabilities.