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

• $$\delta Q∕T<=dS\delta Q_{rev}∕T=dSS:\text{Entropy}$$

  (1.4)

  Into first axiom:

  $$dU=TdS-dW$$

  (1.5)

• $S$ is a state variable

• $U$ is a potential $U(S,...)$ 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 $\Rightarrow$ 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)