Resolving Levinthal's Paradox through Computational Action Minimization: A Causal-Memory Bound on Protein Folding Thermodynamics and Dynamics

Levinthal's paradox highlights the apparent incompatibility between the enormous conformational state space of proteins and the rapid folding times observed in experiment. Modern energy-landscape theory resolves much of this tension by replacing blind search with biased diffusion on a funnel-shaped free-energy surface. Here we extend that picture by introducing a minimal dynamical ingredient motivated by open effective field theory (Open-EFT): a latent state variable obeying a causal relaxation law with a finite memory time \Delta. Within a coarse-grained stochastic thermodynamic description, the reduction of conformational uncertainty during folding implies a minimal irreversible heat dissipation bounded by an information-thermodynamic inequality formally analogous to the Landauer bound. In the dynamical sector, introducing a finite memory timescale renders the effective dynamics weakly non-Markovian and biases trajectory statistics away from rapid trapping by short-scale roughness on the funnel landscape. In the strict Markovian limit (\Delta = 0), the effective coordinate remains maximally sensitive to short-scale landscape roughness, leading in our minimal model to enhanced residence times in local minima and longer mean first-passage folding times. For \Delta > 0, the latent variable introduces a finite relaxation time that effectively smooths short-wavelength roughness of the energy landscape while preserving the large-scale funnel gradient. We report numerical overdamped Langevin simulations of a minimal one-dimensional rough-funnel model that reveal a non-monotonic dependence of the mean first-passage folding time on the memory parameter \Delta, with an intermediate regime in which folding is accelerated relative to both the Markovian and strongly memory-dominated limits. The framework connects naturally with existing Generalized Langevin Equation (GLE) and internal-friction literature, interpreting the memory parameter within the Principle of Computational Action Minimization (PCAM) as an informational relaxation scale that reweights trajectory statistics toward lower computational-action pathways.