Anticipation Series — Paper II: Thermodynamic Dynamics of Anticipation: Dissipation, Relaxation, and the Cost of Staying in Phase

Paper II of the Anticipation Series within the Radial Coherential Dynamics (RCD) research program. ABSTRACT: Paper I established anticipation as counterfactual simulation with thermodynamic cost (LA = Sₐvoided / Sₛim). Here we develop the DYNAMICS: how anticipatory systems maintain coherence against noise in real time. We formulate anticipation as a driven-dissipative process using Langevin dynamics with an explicit metabolic drive term that breaks detailed balance, derive explicit dissipation rates connected to Landauer's principle, and show how Time-Dependent Ginzburg-Landau (TDGL) dynamics governs relaxation after perturbations. The key result is that maintaining N3 (anticipatory) capacity requires continuous entropy export at a rate bounded below by the Landauer limit. We show that the Landauer cost acts as an external field that converts sharp phase transitions into smooth crossovers, with pseudo-critical slowing down near the crossover temperature T*. No conservative Lagrangian is assumed; the treatment remains fully dissipative. Explicit falsification conditions are provided. KEYWORDS: Non-equilibrium thermodynamics, Langevin dynamics, Dissipation, TDGL, Anticipatory systems, Entropy production, Driven-dissipative systems, Crossover phenomena This paper was developed using a collaborative human-AI panel methodology, with technical review provided by Claude (Anthropic), ChatGPT (OpenAI), Gemini (Google DeepMind), Grok (xAI), and Perplexity. Part of a trilogy: - Paper I: Physical Foundations (DOI: 10. 5281/zenodo. 18420495) - Paper II: Thermodynamic Dynamics (this paper) - Paper III: Collective Coherence