Entropy of Memory as a Thermodynamic Cost of Neural Plasticity: A Minimal Theory of Irreversible Engram Writing

Memory formation is widely treated as an information-processing phenomenon, yet biological memory must ultimately be instantiated by physical state changes in an open, dissipative substrate. Here we propose a minimal theoretical framework that treats memory writing as an irreversible thermodynamic operation on an effective synaptic state space. Building on Landauer’s principle for logically irreversible transformations and modern stochastic thermodynamics of information, we derive a lower bound on entropy production per effective logical alternative written, incorporating synaptic degeneracy, coarse-graining, and reconsolidation-driven rewriting. To make these constraints explicit, we introduce a minimal bistable synapse model as a physically grounded one-bit memory and analyze finite-time writing protocols using stochastic dynamics. Numerical simulations show that finite-time and reliability constraints generically raise dissipation above the quasistatic Landauer limit, yielding entropy costs of order 10–50 kBT per reliably written bit for fast, biologically plausible protocols. These results demonstrate how irreversibility emerges even in minimal models, independently of biochemical detail. The framework yields falsifiable predictions: learning tasks matched for spiking activity can differ in entropy production due to different amounts of synaptic rewriting; high-plasticity regimes should exhibit disproportionate metabolic or thermal signatures; and sleep-associated synaptic renormalization should be constrained by cumulative irreversibility. Overall, this work provides a compact thermodynamic interpretation of memory cost that complements mechanistic plasticity theories and clarifies the physical limits of durable memory formation in neural systems.