# Thermomass theory

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The thermomass theory, proposed by Prof. Zeng-Yuan Guo,[1] regards heat owning the mass-energy duality, which exhibits energy-like features in conversion processes or mass-like characteristics in transfer processes.

Thermomass is defined as the equivalent mass of the thermal energy in heat transfer, which is determined by the Einstein’s mass-energy equivalence. The mass of heat therefore leads to the “inertia” and “weight” of heat in heat transfer. Because the mass of heat is extremely small (10^{-16} kg for 1 J heat), it has been seldom measured but may show its significance in ultrafast heating or ultrahigh-rate heat transfer processes. Distinguished from the traditional Caloric theory which treats heat as substance without mass, the thermomass theory treats heat as a flux of substance with mass.[2]

Based on the thermomass theory, a thermomass gas model has been developed.[3] In this model, the heat transfer process can be treated as a thermomass gas flow in medium, driven by a thermomass pressure gradient (a potential field). The thermomass gas is a gas-like collection of massive thermons, which is defined as a unit quasi-particle carrying the thermal energy. For solids, the thermomass gas will be the phonon gas for crystals, attached on the electron gas for pure metals, or just between both for most of other solids. To concern the heat transfer behavior in medium, we only focus on the macroscopic flow characteristics of the thermomass gas rather than the details of each single thermon, and therefore we suppose the thermomass gas as a continuum and its transport process can be described by the classical Newton’s mechanics.

The equation of state and the governing equations for the thermomass gas transport based on methodologies of the classical mechanics lead to the general law of heat conduction to describe the relationship between the heat flux and the temperature field. The general law degenerates to the Fourier’s law if all the thermal inertial effects are negligible, and therefore provides us a new viewpoint to understand the Fourier’s law for heat conduction. The Fourier’s law essentially means the balance between the driving force and the resistant force in the thermomass fluid mechanics. Therefore the Fourier’s law will break down when the inertial effect is not negligible or the linear resistance-velocity relationship is not valid.

The thermal wave phenomena have been studied using the thermomass theory.[4] The general law degenerates to the same form as the Cattaneo-Vernotte model with different physical significances for the characteristic time, when the time dependent parts of the thermal inertial effects are only considered. The characteristic time in the thermomass gas model means the lagging time from the temperature gradient to the corresponding heat flux, while the one in the Cattaneo-Vernotte model is the relaxation time from the thermal non-equilibrium to the equilibrium state. This difference leads to very different predictions for the thermal wave propagation behavior. For the dielectrics, the values of the characteristic time may differ by two orders of magnitude, which results in a much slower temperature response to a heat pulse predicted by the thermomass gas model than that by the CV model. Even for the heat waves in metals, where the two characteristic times are very close, the thermal inertial effects also cause different features of heat wave propagation. Especially the unphysical temperature distribution under zero predicted by the Cattaneo-Vernotte model, when two low-temperature cooling waves meet, will not appear in the predictions by our general law.

The thermomass theory has been applied to predict the anomalous thermal transport properties of nanomaterials. The general law describes the steady-state non-Fourier heat conduction when the time dependent terms are neglected, with the thermal inertial effects considered. The predictions show that the effective thermal conductivity of nanomaterials, which is smaller than the intrinsic one, decreases with the decreasing length for a given temperature difference between ends, and increases with the average temperature for a given length. These results agree with the existing theoretical or experimental data.[5]

Recently the thermomass theory has been compared with the extended irreversible thermodynamics and phonon hydrodynamics theory. As a statistic foundation,[6] it has been found that the convective term in the generalized heat conduction equation based on thermomass theory actually comes from the nonlinear part of the phonon distribution function, thus the derivation can be regarded as a nonlinear solution of the phonon Boltzmann equation, which extends the content of the GK model. For nonequilibrium thermodynamics the thermomass theory presents a modification of the entropy and entropy production, avoiding the paradox of negative entropy production in heat wave propagation.[7][8] Furthermore, the entropy production originates from the establishment of Onsager Reciprocal Relation.So the validation of the reciprocal relation is also made from a thermomass perspective. The concept of generalized forces and fluxes are clarified to remove the controversy of the proof of reciprocal relations, i.e. whether or not the generalized flux can be expressed as the time derivative of certain state variables.[9]