The Boltzmann transport equation and related approaches are important tools in non-equilibrium statistical mechanics due to their extreme simplicity.
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Continuity equations underlie more specific transport equations such as the convection diffusion equation, Boltzmann transport equation, and Navier Stokes equations.
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The standard Boltzmann Transport Equation is obtained when the non-local terms on the LHS disappear in the limit of slow spatial variations.
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Assuming the phonon transport is diffusive and Boltzmann transport equation ( BTE ) is valid, nanowire thermal conductance " G ( T ) " can be defined as:
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At yet larger length scales ( mesoscale, involving many mean free paths ), the Boltzmann transport equation ( BTE ) which is based on the classical Hamiltonian-statistical mechanics is applied.
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The Boltzmann transport equation has been found to be very useful in simulations of electron transport in lightly doped semiconductors ( in transistors ), where the electrons are indeed analogous to a rarefied gas.
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