Editing Loschmidt's paradox (section)

== Origin ==
[[Johann Josef Loschmidt|Josef Loschmidt's]] criticism was provoked by the [[H-theorem]] of [[Boltzmann]], which employed [[kinetic theory of gases|kinetic theory]] to explain the increase of entropy in an ideal gas from a non-equilibrium state, when the molecules of the gas are allowed to collide. In 1876, Loschmidt pointed out that if there is a motion of a system from time ''t''<sub>0</sub> to time ''t''<sub>1</sub> to time ''t''<sub>2</sub> that leads to a steady decrease of ''H'' (increase of [[entropy (classical thermodynamics)|entropy]]) with time, then there is another allowed state of motion of the system at ''t''<sub>1</sub>, found by reversing all the velocities, in which ''H'' must increase. This revealed that one of Boltzmann's key assumptions, [[molecular chaos]], or, the ''Stosszahlansatz'', that all particle velocities were completely uncorrelated, did not follow from Newtonian dynamics. One can assert that possible correlations are uninteresting, and therefore decide to ignore them; but if one does so, one has changed the conceptual system, injecting an element of time-asymmetry by that very action.

Reversible laws of motion cannot explain why we experience our world to be in such a comparatively low state of entropy at the moment (compared to the equilibrium entropy of [[heat death of the universe|universal heat death]]); and to have been at even lower entropy in the past.

Later authors<ref>Waugh, J. S., Rhim, W.-K. and Pines, A.. "Spin echoes and Loschmidt's paradox" Pure and Applied Chemistry, vol. 32, no. 1-4, 1972, pp. 317-324. [https://doi.org/10.1351/pac197232010317]</ref> have coined the term "Loschmitz's demon" (in analogy to [[Maxwell's demon]], see [[Loschmidt's paradox#Information theory|below]]) for an entity that is able to reverse time evolution in a microscopic system, in their case of nuclear spins, which is indeed, if only for a short time, [[Spin echo|experimentally]] possible.

=== Before Loschmidt ===
In 1874, two years before the Loschmidt paper, [[William Thomson, 1st Baron Kelvin|William Thomson]] defended the second law against the time reversal objection in his paper "The kinetic theory of the dissipation of energy".<ref>[[William Thomson, 1st Baron Kelvin|Thomson, W. (Lord Kelvin)]] (1874/1875). [https://archive.org/stream/mathematicalphys05kelvuoft#page/11/mode/1up The kinetic theory of the dissipation of energy], ''[[Nature (journal)|Nature]]'', Vol. IX, 1874-04-09, 441–444.</ref>