Ozone in ozone layer
It does not have much to do with entropy, rather with the way and place of ozone creation.

Stratospheric ozone is produced typically at altitude 20-30 km by UVC radiation with $\lambda \lt \pu{280 nm}$:

$$\ce{O2 + \nu -&gt; 2 O}$$
$$\ce{O + O2 -&gt; O3}$$

See ozone cycle as courtesy of @M. Farooq.

Ozone in lower troposphere troposphere is created by UVB (280-320 nm)  (+UVA >320 nm ??) mostly due catalytic effects of nitrogen oxides that come typically of the oxidative smog of the Los Angeles type:

$$\ce{NO2 + \nu -&gt; NO2^{*}}$$
$$\ce{NO2^{*} + O2  -&gt; NO + O3}$$
$$\ce{2 NO + O2 -&gt; 2 NO2}$$