Relativistic Thermodynamics

Abstract

Abstract. A generally relativistic theory of thermodynamics is developed, based on four main physical principles: heat is a local form of energy, therefore described by a thermal energy tensor; conservation of mass, equivalent to conservation of heat, or the local first law; entropy is a local current; and non-destruction of entropy, or the local second law. A fluid is defined by the thermostatic energy tensor being isotropic. The entropy current is related to the other fields by certain equations, including a generalised Gibbs equation for the thermostatic entropy, followed by linear and quadratic terms in the dissipative (thermal minus thermostatic) energy tensor. Then the second law suggests certain equations for the dissipative energy tensor, generalising the Israel-Stewart dissipative relations, which describe heat conduction and viscosity including relativistic effects and relaxation effects. In the thermostatic case, the perfect-fluid model is recovered. In the linear approximation for entropy, the Eckart theory is recovered. In the quadratic approximation for entropy, the theory is similar to that of Israel & Stewart, but involving neither state-space differentials, nor a non-equilibrium Gibbs equation, nor non-material frames. Also, unlike conventional thermodynamics, the thermal energy density is not assumed to be purely thermostatic, though this is derived in the linear approximation. Otherwise, the theory reduces in the non-relativistic limit to the extended thermodynamics of irreversible processes due to Müller. The dissipative energy density seems to be a new thermodynamical field, but also exists in relativistic kinetic theory of gases.

Entropy of self-gravitating anisotropic matter

“…When matter is not perfect, more general tensor for anisotropic pressure replaces T 0 , for example, elastic solid has anisotropic stress tensor [31]. In the absence of sheer, off-diagonal components of π ab vanishes.…”

Material models of dark energy

“…The theory of non-relativistic solids [60] is very well developed and has many diverse applications, whilst the theory of relativistic solids [61][62][63][64][65] is less developed and has only a few applications, mainly in the description of neutron star crusts [66][67][68][69]. There is also a considerable body of literature pertaining to the construction of the theory of relativistic fluids, see e.g., [70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88] and viscosity effects in cosmology [89][90][91][92][93]. The description of a relativistic perfectly elastic material model of dark energy has already been presented in the literature, for isotropic [94][95][96][97] and anisotropic [98,99] elastic solids.…”

Matter sources of gauge thermodynamics

“…Projection of components along the frame axes as shown in (37) for fourvectors generalizes straightforwardly to tensorial quantities. Let us consider the energy-momentum 3-form built with the eta basis element (A4)…”