The formation of ice in a droplet of supercooled water is an irreversible process. It has been investigated experimentally by measuring the Number N l of droplets of liquid water of volume V at time t out of a total of N 0 liquid droplets at t = 0. The plot ln (N l/N 0) vs. Vt shows a decreasing straight line at short times, which turns downward with increasing t. In order to describe the experimental results, two concepts of irreversible thermodynamics were applied. The first concept is based on the nucleation theory of crystallization and deals with the statistics of the formation of a critical germ, followed by rapid growth to an ice droplet. The binomial and Poisson statistics were used and extended to irreversibility by introducing the time t. In that way it was possible to describe the linear range of the above mentioned plot. From the slope the intensive nucleation rate constant of nucleation J = 2.1 · 10 5 cm − 3 s − 1 was determined at 237 K. The linear range is equally valid for mono-, di- and oligo-nucleation as far as the rate constants J are identical for all types of nucleation. The deviations from the linear plot are due to differences in the rate constants J. Extending the Poisson distribution by some kind of perturbation calculation leads to a new statistics, which completely agrees with the experimental results, both at short times and increased times also. The second concept is based on the theorem of the shortest way, which is a transcription of Hamilton's principle of classical mechanics and the Euler–Lagrange equation of motion to irreversible thermodynamics. It allows the temporal evolution of the entropy S(t) during crystallization of a droplet of supercooled liquid water. Applying this formalism one exactly obtains the same results as nucleation statistics at short times t. This is astonishing, because neither nucleation nor other mechanistic ideas were used for the derivation of the formalism, and moreover the basic concepts of both versions of irreversible thermodynamics are completely different. According to the rate constant of crystallization, the lifetime of a droplet of supercooled liquid is τ = 15 s at 237 K. The rate constant J strongly depends on the temperature T. The experimental results can be reproduced by the phenomenological Arrhenius equation. The plot lnJ vs. 1/T shows an ascending straight line. The slope gives the activation energy E a = − 2.65 · 10 − 18 J at 237 K. In contrast to chemical kinetics, the activation energy is negative, E a < 0. It must be given off to the surroundings, otherwise neither nucleation nor crystallization of a droplet of supercooled water is possible. Hence the critical germ is nothing else than the transition state of crystallization of a water droplet, and the activation energy equals the enthalpy of nucleation E a = ΔH N < 0. In combination with the enthalpy of crystallization ΔH l = − 7.4 · 10 − 21 J of one H 2O molecule at 237 K the number N = 3.6 · 10 2 of molecules can be determined, which are engaged in the formation of the critical germ and the transition state, respectively.