# Boltzmann distribution as an explanation for the 2nd law of thermodynamics

The Wikipedia page for Boltzmann distribution describes it as a distribution of microstates as a function of energy and temperature. From my understanding, the 2nd law of thermodynamics is based on the idea that there are a greater proportion of microstates for some given macrostate (in a combinatorial sense), and this macrostate is thus what is most likely.

Is there an intuitive way to directly use the concept of Boltzmann distribution to explain the 2nd law (i.e. the H-theorem)?

• The H-theorem is not equivalent to the 2nd law of thermodynamics, so using i.e. above is not correct. – Ján Lalinský Feb 4 '19 at 1:08

It is not clear why you think Boltzmann's probability distribution should play a role in derivation of 2nd law. 2nd law states something about possible values of macroscopic constraints like $$V,T$$ at the end of processes that begin and end at some equilibrium state. Boltzmann's distribution depends on such variables as $$V,T$$, but does not place any constraint on them. So the relation is more likely the opposite: from the 2nd law of thermodynamics, or some equivalent (maximum information entropy for isolated system), one can derive the Boltzmann distribution.
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