Non-Markovian Effects in Quantum Tunneling from a Minimal Memory Kernel Model

We introduce a minimal non-Markovian extension of a scalar field model by including a temporal memory kernel with finite relaxation time. The resulting dynamics can be reformulated as a local system with an additional internal degree of freedom. We show that this modification induces history-dependent corrections to quantum tunneling probabilities, leading to a hysteresis effect. An order-of-magnitude estimate suggests that the effect may be observable in tunneling-dominated systems such as nuclear decay.