Artificial intelligence (AI) systems are rapidly becoming more capable, autonomous, and deeply embedded in social life. As humans increasingly interact, cooperate, and compete with AI, we move from purely human societies to hybrid human-AI societies whose collective dynamics cannot be captured by existing behavioural models alone. Drawing on evolutionary game theory, cultural evolution, and Large Language Models (LLMs) powered simulations, we argue that these developments open a new research agenda for social physics centred on the co-evolution of humans and machines. We outline six key research directions. First, modelling the evolutionary dynamics of social behaviours (e.g. cooperation, fairness, trust) in hybrid human-AI populations. Second, understanding machine culture: how AI systems generate, mediate, and select cultural traits. Third, analysing the co-evolution of language and behaviour when LLMs frame and participate in decisions. Fourth, studying the evolution of AI delegation: how responsibilities and control are negotiated between humans and machines. Fifth, formalising and comparing the distinct epistemic pipelines that generate human and AI behaviour. Sixth, modelling the co-evolution of AI development and regulation in a strategic ecosystem of firms, users, and institutions. Together, these directions define a programme for using social physics to anticipate and steer the societal impact of advanced AI.