Statistical Physics has traditionally dealt with entities that interact merely based on the present, and possibly past, configurations. This reactive framework is inefficient in many situations involving living beings, such as predators chasing a prey, pedestrians, or even robots. This paper introduces a statistical physical framework for the dynamics of anticipatory agents, whose present-time dynamics depend on the prospective system state that they anticipate. We clarify how these dynamics can be expressed in terms of a cost function constructed based on observations and we show that the dynamics of an anticipatory agent in d dimensions can be mapped onto the dynamics of a (non-anticipatory) chain in d + 1 dimensions, with fluctuations acting transversely on the chain to account for the uncertainty about the future state. Insights from polymer Physics help us characterize the dynamics of these chains and delineate an anticipation horizon beyond which the blurry future can be handled in a mean-field way. The foregoing framework is successfully applied to pedestrian dynamics, leading to a seamless integration of operational and tactical levels in an agent-based model. Even with a minimal expression of the cost, the model succeeds in reproducing various experimental scenarios which are challenging for state-of-the-art models, such as crossing cluttered environments or alighting from a crowded train. The transparent and flexible basis of the model allows the straightforward incorporation of additional mechanisms.

翻译：统计物理学传统上仅基于当前（可能还有过去）的构型来处理实体之间的相互作用。这种反应性框架在涉及生物体（如捕食者追逐猎物、行人甚至机器人）的许多情境中效率低下。本文提出了一种用于前瞻性智能体动力学的统计物理框架，这些智能体在当前时刻的动态取决于它们所预期的未来系统状态。我们阐明了如何基于观测构建的代价函数来表达这些动力学，并证明了d维空间中前瞻性智能体的动力学可以映射到d+1维空间中（非前瞻性）链状系统的动力学，其中涨落横向作用于链以表征对未来状态的不确定性。来自聚合物物理学的洞见帮助我们表征这些链的动力学，并划分出一个预期视界，超出该视界后模糊的未来状态可以通过平均场方式处理。上述框架成功应用于行人动力学，实现了基于智能体模型中操作层与战术层的无缝融合。即使采用最简形式的代价函数，该模型也能成功复现多种实验场景——这些场景对现有前沿模型而言具有挑战性，例如穿越杂乱环境或从拥挤列车中下车。该模型透明且灵活的基础框架允许直接整合额外的机制。