This paper by Green and Lindsay explores an alternative generalization of classical thermoelasticity, focusing on the inclusion of "second sound" effects. The authors use an entropy production inequality proposed by Green and Laws to derive restrictions on constitutive equations. This work is closely related to Müller's earlier research but provides more explicit results. The theory is linearized, and a uniqueness theorem is stated. Key findings include the symmetry of the linear heat conduction tensor and the allowance for "second sound" effects. The basic equations for a single-phase continuum are presented, along with an entropy inequality that serves as a foundation for the analysis. The paper also discusses the stress tensor, heat conduction vector, and entropy in terms of two scalar functions, aligning with Müller's work while offering a more detailed and explicit formulation.This paper by Green and Lindsay explores an alternative generalization of classical thermoelasticity, focusing on the inclusion of "second sound" effects. The authors use an entropy production inequality proposed by Green and Laws to derive restrictions on constitutive equations. This work is closely related to Müller's earlier research but provides more explicit results. The theory is linearized, and a uniqueness theorem is stated. Key findings include the symmetry of the linear heat conduction tensor and the allowance for "second sound" effects. The basic equations for a single-phase continuum are presented, along with an entropy inequality that serves as a foundation for the analysis. The paper also discusses the stress tensor, heat conduction vector, and entropy in terms of two scalar functions, aligning with Müller's work while offering a more detailed and explicit formulation.