Boltzmann's statistical imperative
Boltzmann provided a statistical argument to show that an isolated system not at maximal entropy will is overwhelmingly likely to evolve toward higher entropy - hence the second law and the thermodynamic arrow.

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The Arrow of Time  »The Arrow of Time 
The physics of time »The physics of time
The thermodynamic arrow »The thermodynamic arrow
Why do we see an entropy gradient? »Why do we see an entropy gradient?
Asymmetric boundary condition »Asymmetric boundary condition
Boltzmann's statistical imperative
Maxwell's demon objection »Maxwell's demon objection
Must observe increasing entropy »Must observe increasing entropy
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