Coordination Requires Simplification: Thermodynamic Bounds on Multi-Objective Compromise in Natural and Artificial Intelligence
This provides a foundational thermodynamic framework explaining coordination bottlenecks across systems from neural networks to bureaucracies, with implications for multi-objective optimization and AI alignment.
The paper tackles the fundamental thermodynamic constraints on multi-objective coordination in information-processing systems, showing that coordination protocols must undergo radical information loss and simplification, with minimum description length scaling as L(P) ≥ NK log₂ K + N²d² log(1/ε) for N agents, d objectives, and precision ε.
Information-processing systems that coordinate multiple agents and objectives face fundamental thermodynamic constraints. We show that solutions with maximum utility to act as coordination focal points have a much higher selection pressure for being findable across agents rather than accuracy. We derive that the information-theoretic minimum description length of coordination protocols to precision $\varepsilon$ scales as $L(P)\geq NK\log_2 K+N^2d^2\log (1/\varepsilon)$ for $N$ agents with $d$ potentially conflicting objectives and internal model complexity $K$. This scaling forces progressive simplification, with coordination dynamics changing the environment itself and shifting optimization across hierarchical levels. Moving from established focal points requires re-coordination, creating persistent metastable states and hysteresis until significant environmental shifts trigger phase transitions through spontaneous symmetry breaking. We operationally define coordination temperature to predict critical phenomena and estimate coordination work costs, identifying measurable signatures across systems from neural networks to restaurant bills to bureaucracies. Extending the topological version of Arrow's theorem on the impossibility of consistent preference aggregation, we find it recursively binds whenever preferences are combined. This potentially explains the indefinite cycling in multi-objective gradient descent and alignment faking in Large Language Models trained with reinforcement learning with human feedback. We term this framework Thermodynamic Coordination Theory (TCT), which demonstrates that coordination requires radical information loss.