The Reversibility Paradox: Role of the Velocity Reversal Step

The reversibility, or Loschmidt paradox, is a thought experiment in which microscopic reversibility is exploited to generate an apparently spontaneous trajectory in which entropy decreases, thus violating the Second Law of Thermodynamics (SLT). To achieve this, the system is allowed to evolve from a low-entropy to a high-entropy configuration, at which point all velocities of its molecules are reversed, thus producing the desired effect. In this paper we focus on the velocity reversal step. Implementing this step requires the measurement of velocities and positions, which must be stored in a memory. Even in the case of a reversible measurement, the erasure of the stored information, necessary to reset the measuring device to its original state, has an entropy cost that offsets the entropy decrease during the reverse evolution of the system. This cost is sufficient to explain why the described procedure does not violate the SLT.