Transient Thermodynamic Efficiency of Adaptive Inference in Continuously Nonstationary Environments

Abstract

Adaptive physical and biological systems continually process fluctuating information from their environments. When the environment is nonstationary, inference itself becomes a nonequilibrium process with thermodynamic cost. We analyse a minimal stochastic model which is an overdamped particle in an adaptive double well potential whose control parameter tracks a drifting Ornstein Uhlenbeck signal. Using stochastic energetics, we derive explicit expressions for entropy production, mutual information rate, and a time dependent learning efficiency. High precision Langevin simulations reveal transient peaks in learning efficiency during rapid environmental shifts, absent in steady state averages. These results identify transient adaptive regimes as moments of maximal information to energy conversion, highlighting that maximal thermodynamic learning performance arises transiently rather than in steady state. Throughout this work, the environment is treated as an externally driven stochastic signal rather than a thermodynamic subsystem under control, and its intrinsic entropy production is therefore excluded from the thermodynamic accounting.

Figures (7)

• Figure 1: Adaptive tracking: The environment signal $E(t)$ (orange) and adaptive parameter $\theta(t)$ (blue) evolve over time.
• Figure 2: Drifting environmental mean $\mu(t)$, representing slow nonstationarity in environmental statistics.
• Figure 3: Instantaneous entropy production rate $\dot S_{\mathrm{tot}}$. Peaks correspond to active control effort during environmental shifts.
• Figure 4: Instantaneous learning efficiency $\eta(t)$. Transient spikes represent brief intervals of high adaptive performance.
• Figure 5: Ensemble-averaged entropy production rate $\langle \dot S_{\mathrm{tot}} \rangle$. Shaded region denotes one standard deviation.