Abstract
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.
Abstract (translated)
信息处理系统在多个代理和目标之间进行协调时面临基本的热力学约束。我们展示了具有最大效用的解决方案作为协调焦点，其对跨代理可发现性有更高的选择压力，而非准确性。我们推导出协调协议的信息理论最小描述长度$ L(P) \geq NK\log_2 K + N^2d^2\log (1/\varepsilon)$，其中对于具有$d$个潜在冲突目标和内部模型复杂度为$K$的$N$个代理而言，其精确度达到$\varepsilon$。这种扩展关系迫使系统逐步简化，并且协调动态改变了环境本身，优化层次也随之变化。从已建立的焦点移动需要重新协调，这会创建持久的亚稳态和滞后效应，直到重大的环境变化通过自发对称性破缺触发相变为止。 我们操作性地定义了协调温度来预测临界现象并估算协调工作成本，在神经网络、餐厅账单到官僚机构等系统中可测量出这些标志。我们将阿罗定理（关于偏好聚合一致性不可能性的理论）的拓扑版本扩展，发现当偏好组合时其递归约束存在。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规模语言模型中的对齐伪造现象。 我们称此框架为热力学协调理论(TCT)，它表明协调需要彻底的信息损失。
URL
https://arxiv.org/abs/2509.23144
