Any of these assumptions may be violated. For example, Boltzmann's collision can be represented as +A_\mathit{w} -> {A_\mathit{v'}}+A_\mathit{w'}</chem>,}} where formula_6 is a particle with velocity "v". Under time reversal formula_6 transforms into formula_8. Therefore, the collision is transformed into the reverse collision by the "PT" transformation, where "P" is the space inversion and "T" is the time reversal. Detailed balance for Boltzmann's equation requires "PT"-invariance of collisions' dynamics, not just "T"-invariance. Indeed, after the time reversal the collision +A_\mathit{w} -> {A_\mathit{v'}}+A_\mathit{w'}</chem>,}} transforms into +A_\mathit{-w'} -> {A_\mathit{-v}}+A_\mathit{-w}</chem>.}} For the detailed balance we need transformation into