Active matter concerns many-body systems comproed of living or self-driven agents that collectively exhibit macroscopic phenomena distinct from conventional passive matter. Using Schwinger-Keldysh effective field theory, we develop a hydrodynamic framework for thermal active matter that accounts for energy balance, local temperature variations, and the ensuing stochastic effects. By modeling active matter as a driven open system, we show that the source of active contributions to hydrodynamics, violations of fluctuation-dissipation theorems, and detailed balance is rooted in the breaking of time-translation symmetry due to the presence of fuel consumption and an external environmental bath. In addition, our framework allows for nonequilibrium steady states that produce entropy, with a well-defined notion of steady-state temperature. We use our framework of active hydrodynamics to develop effective field theory actions for active superfluids and active nematics that offer a first-principle derivation of various active transport coefficients and feature activity-induced phase transitions. We also show how to incorporate temperature, energy, and noise in fluctuating hydrodynamics for active matter. Our work suggests a broader perspective on active matter that can leave an imprint across scales.

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• Active nematics
• Finite temperature field theory
• Living matter & active matter
• Hydrodynamic models