Information-processing systems coordinating across multiple agents and objectives face fundamental thermodynamic constraints. We show that solutions with maximum utility to act as coordination focal points have 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.

翻译：跨多个智能体和目标进行协调的信息处理系统面临着基本的热力学约束。我们证明，作为协调焦点具有最大效用的解，在跨智能体可发现性方面承受的选择压力远高于在精确性方面。我们推导出，对于具有$d$个潜在冲突目标和内部模型复杂度$K$的$N$个智能体，协调协议达到精度$\varepsilon$的信息论最小描述长度按$L(P)\geq NK\log_2 K+N^2d^2\log (1/\varepsilon)$缩放。这种缩放迫使渐进简化，协调动态本身改变环境，并在层次结构间转移优化。从已建立的焦点转移需要重新协调，从而产生持久的亚稳态和滞后现象，直到显著的环境变化通过自发对称性破缺触发相变。我们操作性地定义了协调温度以预测临界现象并估计协调工作成本，识别了从神经网络到餐厅账单再到官僚机构等各类系统中可测量的特征。通过扩展阿罗定理关于一致偏好聚合不可能性的拓扑版本，我们发现每当偏好被组合时，该定理递归地产生约束。这可能解释了多目标梯度下降中的无限循环，以及通过人类反馈强化学习训练的大型语言模型中的对齐伪装。我们将此框架称为热力学协调理论，它证明了协调需要根本性的信息损失。