Loschmidt's Paradox

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?

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