Then Boltzmann s assumption of molecular chaos can be justified.
2.
The necessary assumptions are the absence of quantum effects, molecular chaos and small gradients in bulk properties.
3.
In many cases the molecular chaos assumption is highly accurate, and the ability to discard complex correlations between particles makes calculations much simpler.
4.
However the key assumption he made in formulating the collision term was " molecular chaos ", an assumption which breaks Loschmidt and others over Loschmidt's paradox ultimately ended in his failure.
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In the early 1970s, Manfred Eigen and Peter Schuster examined the transient stages between the molecular chaos and a self-replicating quasispecies, which through natural selection entered into a form of Darwinian evolution.
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In classical thermodynamics, the second law is a basic postulate applicable to any system involving heat energy transfer; in statistical thermodynamics, the second law is a consequence of the assumed randomness of molecular chaos.
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However, if the stochastic behavior of the molecules in actual walls is considered, along with the randomizing effect of the ambient, background thermal radiation, Boltzmann s assumption of molecular chaos can be justified.
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The kinetic equation and in particular Boltzmann's molecular chaos assumption inspired a whole family of Boltzmann equations that are still used today to model the motions of particles, such as the electrons in a semiconductor.
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The explanation is that Boltzmann's equation is based on the assumption of " molecular chaos ", i . e ., that it follows from, or at least is consistent with, the underlying kinetic model that the particles be considered independent and uncorrelated.
10.
Boltzmann made a key assumption known as the " Stosszahlansatz " ( molecular chaos assumption ), that during any collision event in the gas, the two particles participating in the collision have 1 ) independently chosen kinetic energies from the distribution, 2 ) independent velocity directions, 3 ) independent starting points.
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