Hydrodynamics of thermal active matter

TL;DR

This work develops a comprehensive hydrodynamic framework for thermal active matter using Schwinger-Keldysh effective field theory, explicitly modeling energy input from fuel and entropy loss to the environment to capture non-equilibrium steady states with a dynamical temperature $T_0$. It introduces an active KMS symmetry, a famine state limit, and a systematic treatment of fluctuations, enabling controlled violations of fluctuation-dissipation theorems and detailed balance. The framework is applied to active superfluids and active nematics, yielding first-principles active transport coefficients, activity-induced phase transitions, and energy–entropy correlation functions, while embedding temperature and noise consistently in fluctuating hydrodynamics. Overall, the approach provides a symmetry-based, scalable route to describe active phenomena across scales, with potential extensions to a range of driven open systems including polar order, electrically driven fluids, and complex environments.

Abstract

Active matter concerns many-body systems comprised 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 novel hydrodynamic framework for thermal active matter that accounts for energy balance, local temperature variations, and the ensuing stochastic effects. By modelling 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 non-equilibrium 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.

Figures (3)

• Figure 1: Schematic representation of energy balance between the system, fuel reservoir, and environment. Without the environment component, fuel consumption would lead to an indefinite build-up of energy or heat in the system.
• Figure 2: Schematic representation of the famine state. When the fuel reservoir is absent, the system can still exchange heat with the environment and reaches a unique equilibrium state maintained at the environment temperature $T_{\mathsmaller{\mathsf E}}$.
• Figure 3: The effective potential of $\Psi$ in an active superfluid. For $a>0$, the system exists in the spontaneously-unbroken or fluid phase in the absence of activity (black), while for $a<0$ it exists in the spontaneously-broken or fluid phase. For $a/a_{\mathsmaller{\mathsf E}}>0$ (green), increasing activity retains the system in the same phase and drives it further from criticality (red), while for $a/a_{\mathsmaller{\mathsf E}}<0$ (orange), increasing activity eventually flips the potential and induces a phase transition.