Changes

Let the [[linear]], [[angular]] and internal [[momenta]] of a [[molecule]] be given by the set of r variables { pi }. The state of a molecule may then be described by the range δwi = δp1δp2δp3 ... δpr. There are many such ranges [[corresponding]] to different states; a specific state may be denoted by the index i. Two [[molecules]] undergoing a collision can thus be denoted by (i, j) (Such an ordered pair is sometimes known as a [[constellation]].)

Let the [[linear]], [[angular]] and internal [[momenta]] of a [[molecule]] be given by the set of r variables { pi }. The state of a molecule may then be described by the range δwi = δp1δp2δp3 ... δpr. There are many such ranges [[corresponding]] to different states; a specific state may be denoted by the index i. Two [[molecules]] undergoing a collision can thus be denoted by (i, j) (Such an ordered pair is sometimes known as a [[constellation]].)

It is convenient to suppose that two molecules exert a negligible ''effect'' on each other unless their centre of [[gravities]] approach within a critical distance b. A collision therefore begins when the respective [[centres]] of [[gravity]] arrive at this critical distance, and is completed when they again reach this critical distance on their way apart. Under this [[model]], a collision is completely described by the matrix , which refers to the constellation (i, j) before the collision, and the (in general different) constellation (k, l) after the collision.

It is convenient to suppose that two molecules exert a negligible ''effect'' on each other unless their centre of [[gravities]] approach within a critical distance b. A collision therefore begins when the respective [[centres]] of [[gravity]] arrive at this critical distance, and is completed when they again reach this critical distance on their way apart. Under this [[model]], a collision is completely described by the matrix [[File:Collision_matrix.jpg]] , which refers to the constellation (i, j) before the collision, and the (in general different) constellation (k, l) after the collision.

This notation is convenient in proving Boltzmann's [http://en.wikipedia.org/wiki/H-theorem H-theorem] of [http://en.wikipedia.org/wiki/Statistical_mechanics statistical mechanics].[http://en.wikipedia.org/wiki/Collision]

This notation is convenient in proving Boltzmann's [http://en.wikipedia.org/wiki/H-theorem H-theorem] of [http://en.wikipedia.org/wiki/Statistical_mechanics statistical mechanics].[http://en.wikipedia.org/wiki/Collision]

[[Category: Physics]]

[[Category: Physics]]