Resolving inconsistencies in Relativistic Thermodynamics with four-entropy and four-heat current

Abstract

We address long-standing inconsistencies in relativistic thermodynamics, particularly the ambiguities in temperature transformations and entropy evolution in moving or accelerating frames. Traditional approaches often lead to spurious entropy dissipation or generation in accelerating frames, contradicting the second law of thermodynamics. By introducing four-entropy and four-heat current, we resolve the problematic terms related to Lorentz factor dependence, eliminating unphysical entropy production. We also show that transformations like $T^{\prime}=\frac{T}{\gamma}$ and $T^{\prime}=T \gamma$ introduce an additional unphysical source of entropy dissipation or generation without real heat flow, driven by temperature gradients from relative motion. By adopting the covariant transformation $T^{\prime}=T$ and treating heat and entropy as four-vectors, we resolve these inconsistencies and offer a coherent framework for relativistic thermodynamics.