Lorentz Factor and the Carnot Heat Engine

[IDMclean]

I was reading about the Carnot heat engine the other day, and I noticed that Carnot's theorem looked oddly familiar. Like Lorentz factor familiar. I don't have much to say about this, but I do have a question. Is the following equivalence mathematically correct?

 

Lorentz Factor

[math]\gamma =\frac{1}{\sqrt{1-\frac{\nu^2}{c^2}}} = \frac{1}{\sqrt{1-\beta}}[/math]

 

Carnot Efficiency

[math]\eta=1-\frac{T_C}{T_H}=\frac{W}{Q_H}[/math]

 

Hypothetical Lorentz-Carnot Efficiency Factor

[math]\gamma =\frac{1}{\sqrt{1-\frac{\nu^2}{c^2}}} = \frac{1}{\sqrt{\eta}}=\frac{1}{\sqrt{1-\frac{T_C}{T_H}}}=\frac{1}{\sqrt{\frac{W}{Q_H}}}[/math]

 

On a glance over a google search, I found this.

A SPECIAL RELATIVISTIC HEAT ENGINE