This Demonstration proposes a clarification of contradictory theoretical approaches to relativistic thermodynamics. According to our suggestion, a new concept of internal energy leads to thermodynamic equilibrium conditions that incorporate the existing propositions. You can manipulate spacetime vectors related to the intensive parameter

representing energy-momentum equilibration.

In equilibrium, two moving and interacting thermodynamic bodies obey

. In the coordinate system of the first body this condition can be expressed by the spacetime velocity vectors of body centers and energy currents as

and

, respectively. The snapshots show famous particular cases for the relative speed

.

Snapshot 1: the Planck–Einstein equilibrium, when the energy current is carried by the moving body,

; in this case the moving body appears cooler

Snapshot 2: the Blanusa-Ott equilibrium, when the energy current stays with the observing body,

; in this case the moving body appears hotter

Snapshot 3: the Landsberg equilibrium, when the energy current velocities compensate each other inside the two bodies,

; in this case the temperatures of the two moving bodies are equal

Snapshots 4 and 5: the Doppler blue shift and red shift (

) equilibria, when the energy transfer is due to radiation,

,

; in these cases the temperatures of the two moving bodies are related by a Doppler shift