In this equation, the quantum effect is expressed by the -term, and parameter v is the speed of the electrons which obey the
Maxwell-Boltzmann distribution as given in Eq.(8).
By maximizing Q and using (5), one obtains that the Hawking radiation for macroscopic black hole is given by the following
Maxwell-Boltzmann distribution:
Now we are ready to present application of T(x) in probability and thermodynamics using one of the most important distributions which is called
Maxwell-Boltzmann distributionNote that the Arrhenius equation assumes the
Maxwell-Boltzmann distribution, and the relationship would be different for a Fermi gas.
Gatignol, "How to obtain higher-order multivariate Hermite expansion of
Maxwell-Boltzmann distribution by using Taylor expansion?" Zeitschrift fur Angewandte Mathematik und Physik, vol.
He covers a brief history of entropy and the second law of thermodynamics, all you need to know but never dared admit that you already knew, the uniform spatial distribution, the Boltzman distribution, the
Maxwell-Boltzmann distribution, entropy and the second law in the world of marbles, and entropy and the second law in the real world.
(1) and the red side is predominantly determined by the
Maxwell-Boltzmann distribution of kinetic energies.
He showed that the probability for each possible state of motion is an exponential function of the energy required, giving what is now known as the
Maxwell-Boltzmann distribution. Maxwell showed how the phenomena of diffusion, viscosity, and thermal conductivity could be related to molecular transport of mass, momentum, and energy.
For example, in [3, 28],
Maxwell-Boltzmann distribution functions are used to calculate the thermodynamics of photon gas.