 Ignoring historical details (Brush 1976, Frigg &amp; Werndl 2011, Sklar 1993, Uffink 2006), here is the core idea loosely reconstructed from Boltzmann’s later writings. Consider an isolated gas of \(N\) particles in a box, where \(N\) is large enough to make the system macroscopic \((N \approx 10^{23}+)\). For the sake of familiarity we will work with classical mechanics. We can characterize the gas by the coordinates and momenta \(x_{in}, p_{in}\) of each of its particles and represent the whole system by a point \(X = (q,p)\) in a \(6N\)-dimensional phase space known as \(\Gamma\), where \(q = (q_1 \ldots q_{3N})\) and \(p = (p_1 \ldots p_{3N})\). Boltzmann’s great insight was to see that the thermodynamic entropy arguably “reduced” to the volume in \(\Gamma\) picked out by the macroscopic parameters of the system. The key ingredient is partitioning \(\Gamma\) into compartments, such that all of the microstates \(X\) in a compartment are macroscopically (and thus thermodynamically) indistinguishable. To each macrostate \(M\), there corresponds a volume of \(\Gamma\), \(\lvert\Gamma_M\rvert\), whose size will depend on the macrostate in question. For combinatorial reasons, almost all of \(\Gamma\) corresponds to a state of thermal equilibrium. There are simply many more ways to be distributed with uniform temperature and pressure than ways to be distributed with nonuniform temperature and pressure. There is a vast numerical imbalance in \(\Gamma\) between the states in thermal equilibrium and the states in thermal nonequilibrium.