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.

翻译：协调多智能体与多目标的信息处理系统面临着基本的热力学约束。我们证明，作为协调焦点且具有最大效用的解，其在不同智能体间的可发现性（而非精确性）承受着更强的选择压力。我们推导出，对于具有$d$个潜在冲突目标且内部模型复杂度为$K$的$N$个智能体，协调协议达到精度$\varepsilon$所需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。这种缩放迫使系统进行渐进简化，协调动力学本身改变环境，并在层级间转移优化过程。从已建立的焦点转移需要重新协调，从而产生持续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算协调工作成本，识别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。通过扩展阿罗不可能性定理的拓扑版本（关于一致偏好聚合的不可能性），我们发现每当偏好被组合时，该定理便递归地产生约束。这或许可以解释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现象。我们将此框架称为热力学协调理论，它论证了协调必然导致根本性的信息损失。