Relativistic Thermodynamics: A Modern 4-Vector Approach

Abstract

Using the Minkowski relativistic 4-vector formalism, based on Einstein's equation, and the relativistic thermodynamics asynchronous formulation (Grøn (1973)), the isothermal compression of an ideal gas is analyzed, considering an electromagnetic origin for forces applied to it. This treatment is similar to the description previously developed by Van Kampen (van Kampen (1969)) and Hamity (Hamity (1969)). In this relativistic framework Mechanics and Thermodynamics merge in the first law of relativistic thermodynamics expressed, using 4-vector notation, such as ΔUμ = Wμ + Qμ, in Lorentz covariant formulation, which, with the covariant formalism for electromagnetic forces, constitutes a complete Lorentz covariant formulation for classical physics.

Elastic properties of 5d transition-metal carbides: An ab initio study

“…One can use a small strain and calculate the change of energy or stress to obtain elastic constants C i j . In the crystal structures analyzed in this work, an external strain δ from −0.08 to + 0.08 was applied in the directions as explained by Güemez et al [16], associated with deformations: isotropic, tetragonal and orthorhombic.…”

A 4-vector formalism for classical mechanics

“…That formalism will be worked-out in the next section. In this section we review those aspects of the relativistic formalism that are essential to derive the corresponding classical one [17]. In the Minkowski's formulation of relativity, a basic physical magnitude is usually expressed as a four-vector.…”