### 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
$$\delta Q\u2215T<=dS\phantom{\rule{2em}{0ex}}\delta {Q}_{rev}\u2215T=dS\phantom{\rule{2em}{0ex}}S:\text{Entropy}$$ | (1.4) |

Into first axiom:

- $S$ 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
$\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)

$\Rightarrow $
”Everybody has his own definition of entropy”

BUT all are equivalent

© J. Carstensen (Stat. Meth.)