Information and Reaction Balance in Statistical Mechanics

 In a set of previous notes, we obtained equilibrium distributions through reaction balance for specific reactions i.e. for e1+e2=e3+e4. In this note, we argue that “information” plays a role in reaction balance as one utilizes the most uncertain situation namely that all reactions ei+ej=e have the same probability as outcomes in the Maxwell-Boltzmann case. We link this to a factorial scheme for reaction types. In addition, we consider more general cases such as the Bose-Einstein and others in order to show that one again chooses the most uncertain scenario in terms of reaction outcomes (not configurations) subject to physical reaction enhancements or restrictions. For example, for the BE case, one no longer has equal probabilities for each ei+ej=e because there is a physical enhancement  f(e1)f(e2) becomes  f(e1)[1+f(e3)]f(e2)[1+f(e4)], but uncertainty with respect to the outcome of a colliding e1 and e2 is maximized subject to this constraint. In this note, we try to show that reaction balance inherently incorporates the idea of maximum uncertainty (or maximum reaction outcomes) subject to reaction enhancement/restriction constraints. Statistical mechanics usually starts with the idea of maximum uncertainty or number of arrangements whereas we argue one may start with the idea of reaction balance. The latter incorporates maximum uncertainty, not of physical arrangements, but of reaction outcomes in time.