16 The Transformations of S , k iand R
We assume in the remaining sections that temperature is a key variable which is directly connected to many structural properties of materials, and therefore is independent of the velocity of an observer:
T' = T
Given the invariance of temperature we get from section 8 for the transformations of k and R
k' j= k · √ mmmm and mmm R' j= R · √
The two gas constants are thus not cut from the same cloth as the speed of light c jand the Planck constant h . It is therefore not appropriate to set the value of k jto 1, as is done in the system of natural units jwith c , h_bar jand the gravitational constant G .
S j= k · ln (Ω) japplies for physical entropies, where Ω is the inverse of an invariant probability. Therefore entropy transforms the same as the Boltzmann constant k :
S' jj= S · √
Entropies of information theory however are relativistically invariant !