On the Grand Canonical Distribution Method of Statistical Mechanics

Reduced Statistical Density Operators in Canonical and Grand Canonical Ensembles

Starting from Bloch equation for a canonical ensemble, we deduce a set of hierarchy equations for the reduced statistical density operator for an identical many-body system with two-body interaction. They provide a law according to which the reduced density operator varies in temperature. By definition of the reduced density operator in Fock space for a grand canonical ensemble, we also obtain ...

Thermodynamics of hydrogen vacancies in MgH2 from first-principles calculations and grand-canonical statistical mechanics

On the Statistical Mechanics of Alien Species Distribution

Many species of plants are found in regions to which they are alien. Their global distributions are characterised by a family of exponential functions of the kind that arise in elementary statistical mechanics (an example in ecology is MacArthur’s broken stick). We show here that all these functions are quantitatively reproduced by a model containing a single parameter—some global resource part...

Hierarchy Bloch Equations for the Reduced Statistical Density Operators in Canonical and Grand Canonical Ensembles

Starting from Bloch equation for a canonical ensemble, we deduce a set of hierarchy equations for the reduced statistical density operator for an identical many-body system with two-body interaction. They provide a law according to which the reduced density operator varies in temperature. By definition of the reduced density operator in Fock space for a grand canonical ensemble, we also obtain ...

Statistical mechanics of neocortical interactions: Canonical momenta indicators of electroencephalography

A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing large-scale properties of short-term memor...