Equations used by scientists and engineers can be classified into two larger groups: the first group includes deterministic and time-reversible equations, whereas the second includes irreversible and stochastic equations. Chemical kinetics equations belong to the second group, whereas the Hamilton equations of classical mechanics belong to the first group. Usually scientist work with equations of only one group, but sometimes it is needed to study situations that require elements of both classes at once; in such situations we need a new kind of equation that combines determinism, stochasticity, time-symmetry, and irreversibility all at once. Take the phenomenological equation for Brownian motion for the average momentum of a particle contained in a fluid, as illustration \[ \frac{\mathrm{d} p}{\mathrm{d}t} = F_\mathrm{ext} - \frac{\zeta}{m} p . \] The term \( F_\mathrm{ext} \) denotes the external deterministic and time-symmetric force, whereas the second term in the right-hand-si