text: The microscopic "reversing of time" turns at the kinetic level into the "reversing of arrows": the elementary processes transform into their reverse processes. For example, the reaction
  : transforms into 
  and conversely. (Here,  are symbols of components or states,  are coefficients). The equilibrium ensemble should be invariant with respect to this transformation because of microreversibility and the uniqueness of thermodynamic equilibrium. This leads us immediately to the concept of detailed balance: each process is equilibrated by its reverse process.
  This reasoning is based on three assumptions:
  #  does not change under time reversal;
  # Equilibrium is invariant under time reversal;
  # The macroscopic elementary processes are microscopically distinguishable. That is, they represent disjoint sets of microscopic events.
  Any of these assumptions may be violated. For example, Boltzmanns collision can be represented as  where  is a particle with velocity v. Under time reversal  transforms into . 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 Boltzmanns equation requires PT-invariance of collisions dynamics, not just T'-invariance. Indeed, after the time reversal the collision  transforms into   For the detailed balance we need transformation into
    For this purpose, we need to apply additionally the space reversal P. Therefore, for the detailed balance in Boltzmanns equation not T-invariance but PT'-invariance is needed.
  Equilibrium may be not T- or PT-invariant even if the laws of motion are invariant. This non-invariance may be caused by the spontaneous symmetry breaking. There exist nonreciprocal media (for example, some bi-isotropic materials) without T and PT invariance.
  If different macroscopic processes are sampled from the same elementary microscopic events then macroscopic detailed balance may be violated even when microscopic detailed balance holds.
  Now, after almost 150 years of development, the scope of validity and the violations of detailed balance in kinetics seem to be clear.