Time Reversal

To understand this violation of the Second Law of Thermodynamics, we will use the properties of Newton's laws. When the molecule reaches its final extended configuration, we stop time, point the velocity of each atom on each molecule in the opposite direction and start time again.

The molecule travels through the same sequence of configurations as the forward process, only in reverse order. It ends in the initial starting configuration, returning to the past. The molecule would do the exact same thing if we reversed the direction of time, so we use the term time reversal to refer to this flipping of the velocities.

It is useful to know the likelihood of seeing this reverse path of configurations compared with the corresponding forward path. To make a fair comparision, the initial configuration of the reverse process must also be in equilibrium with the surrounding water molecules.

We evaluate the likelihood of this reverse path as if the molecule had first been held fixed at a large end-to-end extension. The molecule is then driven from this initial equilibrium by pushing the ends together.