14 Entropy and the Second Law of Thermodynamics
Of course Planck is right when he says that entropy is closely related to a probability. Strictly speaking, it is the product of k jwith the logarithm of the inverse of a probability:
S j= k · ln(Ω) mmmwhere Ω stands for the inverse of an invariant probability
Entropy S jmust therefore transform the same as k .
In the second part of this work we will show that heat quantities are transformed by multiplying by the root factor. Therefore, the relationship
dS j· T j= dQ
still holds, as the product S · T jtransforms like k · T , i.e., by multiplying by the root factor.
In section 9 we have already seen that the second law of thermodynamics remains valid also for a fast-moving observer. On this point, all authors are for once agreed. The STR respects the arrow of time of physics. To avoid causality contradictions time travel into the past is banned, the tilt angle of the time axes in the Epstein diagram is always less than or equal to 90°.
In the formulation of entropy, the second law reads as follows:
In spontaneously occurring processes ∆S j≥ 0 is always true. For all irreversible
processes entropy increases,
for reversible ones it remains constant.
What would change about this statement, if it were true that T' j= T jand jS' j= S · √ ?
∆S j≥ 0 is equivalent to ∆S · √ ≥ j0 which is the same as ∆S' j ≥ 0
The positive square root term changes nothing on the inequality. The second law and the arrow of time are not jeopardized by the transformation of entropy.