Statistical Mechanics and thermodynamics are the basis for a huge amount of technology and scientific models of the world, yet they rely on a fundamental assumption which is in some sense unjustified, known as the 'Ergodic hypothesis': Even though (classically) we know that the current position of gas particles in a box can be determined from their positions in the past, in thermodynamics we make the (unjustified) assumption that their positions are actually random and independent of their previous positions. In other words, these models for the world are probabilistic, which contradicts our more fundamental models of the world which say it is deterministic (and even QM is deterministic, with the single exception of the born rule). What he's doing here helps justify the probabilistic treatment, and understand when it does or does not apply.
I have always though this to be one of the great 'foundations' questions in physics (The others being QM foundations/origin of the born rule, and foundations of Field Theory). These are 'hard' and borderline philosophical questions, which most scientists (with good reason) simply assume to be true, to the point they often find them uninteresting. Lately though there seems to be renewed interest in them.