1.4 Second Axiom of Thermodynamics: Irreversible Processes exist

• A System never changes by its own into a less probable state
• There exists no perpetuum mobile of second kind
•  $\delta Q∕T<=dS\phantom{\rule{2em}{0ex}}\delta {Q}_{rev}∕T=dS\phantom{\rule{2em}{0ex}}S:\text{Entropy}$ (1.4)

Into first axiom:

 $dU=TdS-dW$ (1.5)
• $S$ is a state variable
• $U$ is a potential $U\left(S,...\right)$ for reversible processes
• $dU$ is a total differential
• $S$ increases until thermodynamic equilibrium is reached and afterwards it always has its maximal value; thermodynamic potentials only apply for equilibrium

This knowledge opened the way to heat transforming machines $⇒$ optimization of the efficiency
Thermodynamic is a ”perfect mathematical game”: Based on a minimal set of axioms many results are concluded (many different relations contain the same physical information)

$⇒$ ”Everybody has his own definition of entropy”
BUT all are equivalent