Microscopic time reversibility is one of the foundational assumptions of both classical mechanics and quantum mechanics. A careful quantum analysis shows that reversibility fails even in the most ideal conditions - the case of two particles in collision - when the quantum mechanical interaction with radiation is taken into account.

In quantum mechanics, microscopic time reversibility is assumed true by some scientists because the deterministic linear Schrödinger equation itself is time reversible. But the Schrödinger equation only describes the deterministic time evolution of the possibilities and probabilities of various quantum events.

When an event occurs, if there is a record of the event (if new information enters the universe), the probabilities of multiple possible events collapse to the actual occurrence of one event. In quantum mechanics, this is the irreversible collapse of the wave function. An irreversible event that leaves a record (new information) is often described as a measurement. Measurements are fundamentally and irreducibly irreversible.

When particles collide, even structureless particles should not be treated as individual particles with single-particle wave functions, but as a single system with a two-particle wave function, because they are now entangled.

Treating two atoms as a temporary molecule means we must use molecular, rather than atomic, wave functions. The quantum description of the molecule now transforms the six independent degrees of freedom into three for the molecule's center of mass and three more that describe vibrational and rotational quantum states.

The possibility of quantum transitions between closely spaced vibrational and rotational energy levels in the "quasi-molecule' introduces indeterminacy in the future paths of the separate atoms. The classical path information needed to ensure the deterministic dynamical behavior has been partially erased. The memory of the past needed to predict the future has been lost.

Even assuming the practical impossibility of a perfect classical time reversal, in which we simply turn the two particles around, quantum physics requires two measurements to locate the two particles, followed by two state preparations to send them in the opposite direction, each subject to the Heisenberg indeterminacy principle, which puts calculable limits on the accuracy with which perfect reversed paths can be achieved.

Let us assume this impossible task can be completed, and it sends the two particles into the reverse collision paths. But on the return path, there is only a finite probability that a "sum over histories" calculation will produce the precisely reversed quantum transitions between vibrational and rotational states that occurred in the first collision.

Thus a quantum description of a two-particle collision establishes the microscopic irreversibility that Ludwig Boltzmann sometimes described as his assumption of "molecular disorder." In his second (1877) derivation of the H-theorem, Boltzmann used a statistical approach and the molecular disorder assumption to get away from the time-reversibility assumptions of classical dynamics.