Scaling properties in off-equilibrium dynamical processes

In this paper, we analyze the consequences of scaling hypotheses on dynamic functions, such as two-time correlations C(t,t^'). We show, under general conditions, that C(t,t^') must obey the scaling behavior C(t,t^')=φ₁(t)^f(β)S(β), where the scaling variable is β=β(φ₁(t^')/φ₁(t)) and φ₁(t^'),φ₁(t) are two undetermined functions. The presence of a nonconstant exponent f(β) signals the appearance of multiscaling properties in the dynamics.