Reversibility and potentiality of exclusion processes on countable discrete groups

Transition invariant exclusion processes on discrete groups, as examples of spatially extended systems, are discussed in this work. We show that there is reversibility if and only if the entropy production vanishes, or iff the speed function field has some bounded potential, which is expressed in terms of physical states rather than mathematical states in probability space. Moreover, we conclude that the only possible bounded potential is the constant one.