Question

explain the term phase space and phase cell​

Answer 1

Phase space

The phase space of a two-dimensional system is called a phase plane, which occurs in classical mechanics for a single particle moving in one dimension, and where the two variables are position and velocity.

Phase cell

Mitosis is the phase of cell division, during which a “parent cell” divides to create two “daughter cells.” The longest part of the cell cycle is called “interphase” – the phase of growth and DNA replication between mitotic cell divisions.

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Answer 2

A space which combines the three coordinates of position space and three coordinates of momentum space is called the phase space and if the volume of the whole phase space is divided into infinitesimally small volumes, then each unit of infinitesimally small volume is called the phase cell.

Explanation:

• The position of any particle can be given as $\[\left( {x,y,z} \right)\]$ in XYZ coordinate system and called position space.
• Similarly, the momentum of that particle can be given by $\left( {{p_x},{p_y},{p_z}} \right)$ and called momentum space.
• Complete information of dynamics of a particle is given by its position plus its momentum that is by $\[\left( {x,y,z} \right)\]$ and $\left( {{p_x},{p_y},{p_z}} \right)$.
• A space which combined the position space and momentum space is called phase space.
• It is a hypothetical space with six-axis perpendicular to each other and a point in phase space is given by the six-coordinate which gives complete dynamics of a particle.
• Now discredited each coordinate of phase space in values of $dx,dy,dz,d{p_x},d{p_y},d{p_z}$, then, the smallest volume of phase cell is given by

       $d\tau = dxdydzd{p_x}d{p_y}d{p_z}$

• Now if the whole phase space is divided into patches of units of volume $d\tau$, then each patch is called the cell of phase space.

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