在微纳尺度导热及超快速加热等极端条件下，经典的傅里叶导热定律已经失效，与对傅里叶导热定律进行补充或修正的方法不同，热质理论重新审视热量的本质，指出热量具有能质二象性，将因热能而使物质分子增加的额外质量称为热质。热量的传递过程实际上就是热质的质量输运过程，并引入动力学方法对于热质输运规律进行了刻画，从而得到了能够描述非傅里叶导热现象的普适导热方程。由于普适导热方程中既有不可逆过程参数，又有可逆过程参数, 是否与现有相关理论相一致; 普适导热方程是阻尼的波动方程，热波的本质是什么; 普适导热方程是基于爱因斯坦质能关系导出的，它是否符合狭义相对论原理。，因此需要对了热质理论作进一步的分析, 並讨论它的应用。非平衡可逆-不可逆过程耦合普适方程理论（GENERIC）是将各种非平衡输运过程分为可逆过程和不可逆过程，并分别用哈密尔顿动力学和耗散势能加以描述。将热质理论应用于GENERIC理论中，所得到描述热质输运的时间演化方程与基于热质流体动力学的普适导热方程具有相同的方程结构，证明了这两种理论的相容性。在此基础上对热质流动过程中的应变率张量和粘性效应进行了研究，进一步完善了普适导热定律的方程架构。热质在传递过程中的具有惯性，从而必将形成热波。对热波本质的分析表明，热量的波动传递和扩散传递都能形成介质中的温度波形, 而且在波动传递过程中。当边界上没有净热流输入时介质中只有热质能的传递, 而没有净热量(热质)的传递，。然后，对热波的矢量效应和界面效应进行了分析，建立了适用于波动传热方程的交替方向隐式差分算法。波动方程的温度表征可能会遗失热波的方向信息，而初始热流分布对热量的传递行为有着重要影响。热波在界面处会发生折射与反射现象，其规律符合菲涅尔定律对于机械波传递规律的刻画，并提出了适用于理想界面的热波弹道能量透射率模型。普适导热定律对于热量传递波动行为的描述对应于声子输运过程中的弹道输运模式和声子水动力学输运模式。基于声子蒙特卡洛算法，求解了声子玻尔兹曼方程，验证了声子水动力学热波的波动行为的存在，并且计算了单声子支作用下的声子水动力学导热过程中的瞬态和稳态导热现象，厘清了弹道热波与声子水动力学热波的不同导热特征，并且构建了初步的声子水动力学稳态导热介观模型。基于爱因斯坦的质能方程推导得到了洛伦兹变换, ，从而证明了质能观和时空观的统一性，因此，基于爱因斯坦质能关系热质理论同时也符合狹义相对论原理，普适

Classical Fourier law fails in describing the heat conduction phenomena in nanoscale mechanism and ultrafast heating process, requiring non-Fourier heat conduction theories. The Einstein’s mass-energy equation implies the unity between energy and mass. The thermomass theory reveals the mass-energy duality of heat, which demonstrates that heat behaves as mass in transport process and behaves as energy in transition process. The extra mass based on molecular vibration is called thermomass. And the heat conduction can be regarded as the mass transport of the thermomass in the media and dealt with in dynamical methods. In this way, the general heat conduction equation, which describes the non-Fourier heat conduction effect, is derived. This paper analyzes the reasonability of thermomass theory in the view of the equation structure, the thermal inertial effect and the relativity theory, respectively and applies the general heat conduction equation and thermomass energy in phonon hydrodynamics and Maxwell’s demon problem.The General Equation for Non-Equilbirum Reversible-Irreversible Coupling (GENERIC) theory divides the nonequilibrium process into the reversible part and irreversible part, and depicts these two parts with Hamiltonian mechanics and dissipation potential, respectively. This paper applies the thermomass theory in the framework of GENERIC and obtains the time evolution equations of thermomass transport. It is found that these equations have the same equation structure as the general heat conduction equation in thermomass dynamics, showing the compatability of these two theories. Meanwhile, the strain tensor and the viscous effect of thermomass transport are studied, which extends the equaitons of thermomass theory.The wavelike behaviors in heat conduction arise from the inertial effect of thermomass. This paper distinguishes the temperature profile wave and thermal wave and points out that the thermal wave and thermomass energy still spread in the media when no net heat flux is applied to the periodic boundary. Then, the vector effect and interfacial effect of thermal wave are analyzed and a new numerical algorithm for hyperbolic heat conduction based on staggered grids is proposed. The temperature representation of hyperbolic heat conduction equations might misses the direction information of heat flux and the intial heat flux has an important influence on the thermal transport. The thermal wave is reflected and refracted at the interface, which is demonstrated to follow the Fresnel’s law. A theoretical model for the interfacial transmission ratio of the thermal wave ballistic thermal energy has been proposed.The general heat conduction equation describes the wavelike behaviors of heat transport and can be applied in the phonon hydrodynamics and ballistic heat conduction. The phonon Boltzmann equation has been solved in phonon hydrodynamic regime by the phonon Monte Carlo simulations. The wavelike behaviors of heat are verified and the transient and steady heat conduction phenomena in phonon hydrodynamics under single phonon branch are studied. The different heat conduction characteristics between ballistic thermal wave and hydrodynamic thermal wave are distinguished and the theoretical mesoscopic models for steady phonon hydrodynamic heat conduction are established.The relativity mass-energy equation lays the foundation of thermomass theory. Via the mass-energy equation, the relativity time-space relation has been derived without the Lorentz transformation. It reveals the unity between mass-energy relation and time-space relation. Thus, the thermomass theory based on mass-energy relation satisfies the time-space relation as well. Then, the application of thermomass energy is analyzed in Maxwell’s demon problem and the information energy is proposed as a new kind of relativity energy. The relativity energy follows the relativity energy conservation law in the energy transport and transition processes.