from https://en.wikipedia.org/wiki/Loschmidt%27s_paradox <<Loschmidt's paradox, also known as the reversibility paradox, irreversibility paradox or Umkehreinwand,[1] is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics. This puts the time reversal symmetry of (almost) all known low-level fundamental physical processes at odds with any attempt to infer from them the second law of thermodynamics which describes the behaviour of macroscopic systems. Both of these are well-accepted principles in physics, with sound observational and theoretical support, yet they seem to be in conflict, hence the paradox. Josef Loschmidt's criticism was provoked by the H-theorem of Boltzmann, which employed 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 t0 to time t1 to time t2 that leads to a steady decrease of H (increase of entropy) with time, then there is another allowed state of motion of the system at t1, 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 universal heat death); and to have been at even lower entropy in the past.>>
Harry On Fri, Feb 28, 2020 at 1:14 PM H LV <hveeder...@gmail.com> wrote: > 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?>> > > > >
