Abstract The discontinuous Lagrangian approach, allowing for a variational description of irreversible phenomena in continuum theory such as viscosity and thermal conductivity, is utilised for the analysis of damped acoustic waves. Starting from a Lagrangian for general viscous flow theory, by linearisation of the resulting Euler–Lagrange equations and performing an ensemble average, a single wave equation for the density perturbations is obtained, being the one resulting from classical Navier–Stokes theory with an additional term due to thermodynamic non-equilibrium. By considering harmonic waves, the respective non-classical dispersion relation and its implications are analysed.

中文翻译：

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暗示阻尼声波非平衡色散关系的不连续变分原理

摘要 不连续拉格朗日方法允许对连续介质理论中的不可逆现象（如粘度和热导率）进行变分描述，用于分析阻尼声波。从一般粘性流理论的拉格朗日算子开始，通过对所得到的欧拉-拉格朗日方程进行线性化并进行系综平均，可以获得密度扰动的单个波动方程，这是经典纳维-斯托克斯理论得出的一个附加项由于热力学不平衡。通过考虑谐波，分析了各自的非经典色散关系及其含义。