## Statistical Physics

If there are small number particle then their equation of
motion may be solved using Newton’s law of motion then they are known as
microscopic system and the solution technique dynamical variable technique

Statistical Physics | Position space | Momentum space |

If there are large number of particle the equation of motion
of all these particle may not be solved simultaneously due to our mathematical
incapability the collection of large number of particle is called macroscopic
system

A gaseous system consist large number of particles hence gaseous
system may be solved by macroscopically i.e either emplying thermodynamics or
statical mechanicque in thermodynamics kinetic theory of gases and law of
thermodynamics is used to determine the thermodynamics variable pressure,
volume, temperature, entropy however in statistical mechanicque the problem may
be solved either Maxwell Boltzmann Boltzmann Einstein statistical and Fermi drack
statics for quantum particle

## Position space

It is a real space in which instantinus statics state of
particle having degree of freedom is represented by their position coordinates
x,y,z

## Momentum space

It is a real space in which instantaneous dynamic state of
any particle having three degree of freedom is represented by three momentum
coordinates thus for a particle 3D of freedom is represented by the position
coordinates x,y,z and three momentum coordinates Px, Py, Pz thus for a three
degree of freedom the phase space would be six dimensional space

In figure along x-axis the position coordinates Q the
momentum coordinates along y-axis for particle having one degree of freedom is
shown

## Dimension of phase space

If we have particle having ‘f’ degree of freedom which means
that to represented that particle in phase space there must be ‘f’ position
coordinates and ‘f’ momentum coordinates therefore in phase space the particle
is represented by 2f coordinates hence the phase space would be 2f dimensional

Classification of phase space

There are two type of phase space

### (A) µ-space

To represented a particle having 3D of freedom µ-space may
be used in which each particle is represented by a phase point in a six
dimensional space therefore in µ-space ‘n’ number of particle are represented
by N phase point such that each phase point have three position coordinates and
three momentum coordinates

### (B) lambda and gamma-space

In gamma space n-particle (identical) are represented by a
single phase point having 3N-position coordinates and 3N-momentum coordinates
thus for a three degree of freedom and N-particle gamma space would 6N
dimension we can also say that gamma space may be constracted from µ space

#### Phase point

In a phase space a particle is represented by position and momentum coordinates with a
point called phase point

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