||We address energy-efficient placement of data and analytics components of composite analytics services on a wireless network to minimize execution-time energy consumption (com- putation and communication) subject to compute, storage and network resource constraints. We introduce an expressive analytics service hypergraph model for representing k-ary composability relationships (k ≥ 2) be- tween various analytics and data components and leverage binary quadratic programming (BQP) to minimize the total energy consumption of a given placement of the analytics hypergraph nodes on the network subject to resource availability constraints. Then, after defining a potential energy functional Φ(·) to model the affinities of analytics components and network resources using analogs of attractive and repulsive forces in physics, we propose a decentralized Metropolis Monte Carlo (MMC) sampling method which seeks to minimize Φ by moving analytics and data on the network. Although Φ is non-convex, using a potential game formulation, we identify conditions under which the algorithm provably converges to a local minimum energy equilibrium placement configuration. Trace-based simulations of the placement of a deep-neural- network analytics service on a realistic wireless network show that for smaller problem instances our MMC algorithm yields placements with total energy within a small factor of BQP and more balanced workload distributions; for larger problems, it yields low-energy configurations while the BQP approach fails.