see http://mw.concord.org/modeler1.3/mirror/thermodynamics/loschmidt.html for animation illustrating Loschmidt`s paradox. When the animation pauses the directional arrow of each particle's velocity is reversed. This shows that the entropy of a closed system does not always increase according to the microscopic laws of physics. In other words the arrow of time cannot simply be explained as a statistical effect of the laws of thermodynamics. Loschmidt posed this paradox as a criticism of Boltzmann's kinetic theory of gases. One way to resolve the paradox is to go beyond the laws of thermodynamics and insist that the universe we know began in a state of maximally low entropy but why it was so has not be explained.
Quote from site <<Loschmidt's Paradox: Can the Second Law of Thermodynamics be violated in molecular dynamics simulations? Loschmidt's Paradox (also known as the Reversibility Paradox) claims that it is not possible to deduce an irreversible process from time-symmetric dynamics such as the classic dynamics. This puts the time reversal symmetry of almost all known low-level fundamental physical laws at odds with any attempt to infer from them the Second Law of Thermodynamics. Loschmidt's Paradox can be illustrated by a simple molecular dynamics simulation. The following model shows that if we reverse the velocities of every single atom in an isolated system (something we can easily do in a computational experiment but hardly possible in reality), the simulation can be exactly reversed. Note that velocity reversal is equivalent to time reversal, as velocity is the first derivative of position against time. Now, an interesting question arise: does the reversible simulation break the Second Law of Thermodynamics?>>
