Some remarks on the boltzmann and anti-boltzmann equations

The derivation of the familiar Boltzmann equation from the mechanical equations of motion of an isolated system is. a problem of long standing. Of particular interest is the question of bow the transition from overall reversibility to irreversibility is dealt with and recent papers by Adams (1960) and by Cohen and Berlin (1960) have drawn attention to the so-called anti-Boltzmann equation which appears somewhat paradoxical. Adams argues that the Boltzmann equation may only be used for prediction, and the anti-Boltzmann equation for retrodiction. The present paper suggests that a generalized Boltzmann-Langevin equation helps to resolve any paradox, and it is shown that either the Boltzmann-Langevin or anti-Boltzmann-Langevin equation may be used for prediction or retrodiction. It remains true that the Boltzmann (-Langeviu) equation is the natural choice for prediction when apparently irreversible behaviour is present.