We introduce a physically grounded framework for coordination in a population based on information constrained feedback in a partially observed stochastic dynamical system. Population size evolves as a continuous time birth death Markov process whose transition rates respond to a shared stochastic measurement signal correlated with the underlying population state. Individuals neither communicate directly nor optimise strategies; instead, coordination emerges from macro to micro feedback mediated by imperfect common information. We show that geometric Brownian motion arises as a limiting case of the conditional dynamics when measurement strength and population statistics satisfy suitable conditions. More generally, varying the signal to noise properties of the measurement channel produces a wider class of stochastic growth processes, including diffusive and jump like regimes, even though ensemble average growth remains exponential. In an appropriate limit the framework recovers the stochastic multiplicative growth model of Peters and Adamou, providing a physical interpretation of coordination as inference and feedback under partial observability.

翻译：我们提出一个基于物理的群体协调框架，该框架依赖于部分可观测随机动态系统中信息受限的反馈。群体规模作为一个连续时间出生-死亡马尔可夫过程演化，其转移速率响应与潜在群体状态相关的共享随机测量信号。个体既不直接通信也不优化策略，而是通过不完美公共信息介导的宏观到微观反馈涌现出协调行为。我们证明，当测量强度与群体统计量满足适当条件时，几何布朗运动作为条件动力学的极限情形出现。更一般地，改变测量通道的信噪比特性可产生更广泛的随机增长过程（包括扩散型与跳跃型动态），尽管系综平均增长仍保持指数形式。在适当极限下，该框架可还原Peters与Adamou的随机乘性增长模型，从而为部分可观测条件下的推断与反馈提供协调的物理解释。