In statistical mechanics, fluctuations are treated as dynamical processes producing correlations between fluctuations at points separated in space and time. The duality between points and tangents of convex functions is reflected in thermodynamics as a duality between extensive and intensive variables. State space is a mathematical space of the values of state variables; each point of the space represents a possible state of equilibrium. Irreversibility is the central message of thermodynamics; the sooner that recognition is made, the better. The mere phrase "second law of thermodynamics" is often enough to produce in students a certain state of unease. The O. Sackur - H. Tetrode formula provides experimental confirmation—from thermodynamic measurements—of the quantum-mechanical picture that particle carries with it a fundamental volume of phase space. Entropy, like quantum mechanics and relativity, is outside everyday experience of the physical world, and must be learned through concerted reflection.