In thermodynamics, Loschmidt’s paradox states that according to the laws of mechanics, a system of particles interacting with any force law, which has gone through a sequence of states starting from some specified initial conditions, will go through the same sequence in reverse and return to its initial state if one reverses the velocities of all the particles; and that this conflicts with the second law of thermodynamics, which asserts that for any such sequence of states the entropy must always increase, meaning that such a system cannot be reversed back to its initial state. [1]

The reversibility paradox was pointed out by Austrian physical chemist Joseph Loschmidt in 1876 to Austrian physicist Ludwig Boltzmann in commentary on his 1872 paper on his H-theorem. In short, Loschmidt said that the H-theorem singled out the direction in time in which H decreases, whereas the underlying mechanics was the same whether time flowed forwards or backwards. [2]

See also
● Poincaré recurrence theorem

References
1. Boltzmann, Ludwig. (1877). “On the Relation of a General Mechanical Theorem to the Second Law of Thermodynamics” (“Uber die Beziehung eines Allgemeine Mechanischen Satzes zum zweiten Hauptsatze der Warmetheorie”), Sitzungsberichte Akad. Wiss., Vienna, Part II, 75: 67-73.
2. Flamm, Dieter. (1999). “Boltzmann: a Disordered Genius”, PhysicsWorld.com, 9 April.

External links
● Loschmidt’s paradox – Wikipedia.