Active materials are characterized by continuous injection of energy at the microscopic level and typically cannot be adequately described by equilibrium thermodynamics. Here we study a class of active fluids in which equilibrium-like properties emerge when fluctuating and activated degrees of freedom are statistically decoupled, such that their mutual information is negligible. We analyse three paradigmatic systems: chiral active fluids composed of spinning frictional particles that are free to translate, oscillating granular gases and active Brownian rollers. In all of these systems, a single effective temperature generated by activity parameterizes both the equation of state and the emergent Boltzmann statistics. The same effective temperature, renormalized by velocity correlations, relates viscosities to steady-state stress fluctuations via a Green–Kubo relation. To rationalize these observations, we develop a theory for the fluctuating hydrodynamics of these non-equilibrium fluids and validate it through large-scale molecular dynamics simulations. Our work sheds light on the microscopic origin of odd viscosities and stress fluctuations characteristic of parity-violating fluids, in which mirror symmetry and detailed balance are broken.

活性材料的特点是在微观水平上连续注入能量，通常不能用平衡热力学来充分描述。在这里，我们研究了一类活性流体，其中当波动和激活的自由度在统计上解耦时会出现类似平衡的特性，因此它们的互信息可以忽略不计。我们分析了三个典型系统：由可自由平移的旋转摩擦粒子组成的手性活性流体、振荡的粒状气体和活性布朗辊。在所有这些系统中，活动产生的单个有效温度参数化了状态方程和涌现的玻尔兹曼统计。相同的有效温度，通过速度相关性重新归一化，通过 Green-Kubo 关系将粘度与稳态应力波动联系起来。为了使这些观察结果合理化，我们为这些非平衡流体的波动流体动力学开发了一种理论，并通过大规模分子动力学模拟对其进行了验证。我们的工作揭示了奇偶性流体的奇数粘度和应力波动特征的微观起源，其中镜像对称性和详细平衡被打破。