Search results
Results from the WOW.Com Content Network
The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for
The statistical entropy perspective was introduced in 1870 by Austrian physicist ... is the microcanonical partition function is the canonical partition ...
The state volume function (used to calculate entropy) is given by v ( E ) = ∑ H i < E 1. {\displaystyle v(E)=\sum _{H_{i}<E}1.} The microcanonical ensemble is defined by taking the limit of the density matrix as the energy width goes to zero, however a problematic situation occurs once the energy width becomes smaller than the spacing between ...
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution.
From the partition function, one can calculate the Helmholtz free energy = and, from that, all the thermodynamic properties of the system, like the entropy, the internal energy, the chemical potential, etc.
These three equations, along with the free energy in terms of the partition function, = , allow an efficient way of calculating thermodynamic variables of interest given the partition function and are often used in density of state calculations. One can also do Legendre transformations for different systems. For example, for a system with a ...
In statistical mechanics, the translational partition function, is that part of the partition function resulting from the movement (translation) of the center of mass. For a single atom or molecule in a low pressure gas, neglecting the interactions of molecules , the canonical ensemble q T {\displaystyle q_{T}} can be approximated by: [ 1 ]
This is almost the partition function for the -ensemble, but it has units of volume, an unavoidable consequence of taking the above sum over volumes into an integral. Restoring the constant C {\displaystyle C} yields the proper result for Δ ( N , P , T ) {\displaystyle \Delta (N,P,T)} .