If the fluctuations of \ beta are characterized by a distribution f ( \ beta ), the " superstatistical Boltzmann factor " of the system is given by
12.
The Liouville measure restricted to the energy surface ? is the basis for the averages computed in Boltzmann factor exp ( & minus; ? " H " ).
13.
The Maxwell Boltzmann distribution applies to any system composed of atoms, and assumes only a canonical ensemble, specifically, that the kinetic energies are distributed according to their Boltzmann factor at a temperature " T ".
14.
We then substitute the energy of each state with its relative probability according to the Boltzmann Factor ( the property of a Boltzmann distribution that the energy of a state is proportional to the negative log probability of that state ):
15.
Under normal circumstances, any particle is more likely to be in a lower-energy state a than higher-energy one, and the ratio between these probabilities is a function of temperature, known as the Boltzmann factor.
16.
The thermodynamic characterisation of systems in equilibrium got its microscopic justification from equilibrium statistical mechanics which states that for a system in contact with a heat bath the probability to find it in any specific microstate is given by the Boltzmann factor.
17.
:: : : The real purpose of this article seems to be to derive the Boltzmann factor, not just the partition function ( see the context in Partition function ( statistical mechanics ); this article was likely forked from there.
18.
This can be understood conceptually as fixing the location of all molecules in the system and then inserting a particle of species i at all locations through the system, averaging over a Boltzmann factor in its interaction energy over all of those locations.
19.
The ratio of oxidized to reduced molecules,, is equivalent to the probability of being oxidized ( giving electrons ) over the probability of being reduced ( taking electrons ), which we can write in terms of the Boltzmann factor for these processes:
20.
In this situation, the expression for the Boltzmann factor fits mathematically with a negative temperature, but this doesn't really count because the system isn't in thermal equilibrium . ) Arbitrary username 16 : 37, 27 June 2006 ( UTC)
