Foremost, surprisal analysis identifies the state of a system when it reaches its maximal entropy, or thermodynamic equilibrium. This is known as balance state of the system because once a system reaches its maximal entropy, it can no longer initiate or participate in spontaneous processes. Following the determination of the balanced state, surprisal analysis then characterizes all the states in which the system deviates away from the balance state. These deviations are caused by constraints; these constraints on the system prevent the system from reaching its maximal entropy. Surprisal analysis is applied to both identify and characterize these constraints. In terms of the constraints, the probability P ( n ) of an event n is quantified by