Fluctuation scaling, an emergent property in complex systems, is expressed by the relationship \(\varXi _{2}\sim M_{1}^{\alpha _{TFS}}\) , connecting the variance ( \(\varXi _{2}\) ) and mean ( \(M_{1}\) ) from empirical data. Utilizing the path integral formalism by H. Kleinert, we explore the origin and temporal evolution of the temporal fluctuation scaling exponent, denoted as \(\alpha _{TFS}(t)\) . Thus, by introducing a non-linear term in the cumulant generating function, \(\mathcal {H}^{(n)}(p,t;\gamma)\) , where n denotes the moment order, we create a model allowing arbitrary evolution of probability distribution moments. Thence, the temporal fluctuation scaling is then described through a linear combination of \(\mathcal {H}^{(n)}(p,t;\gamma)\) with \(n\in {1,2}\) , providing an analytical expression for the evolution of \(\alpha _{TFS}(t)\) . Additionally, a power-law relation, termed temporal Theil scaling, is established between the Theil index T and the mean \(M_{1}(t)\) , being similar to the Ginzburg-Landau theory’s order parameter-temperature relation. Finally, the proposed approach is validated across diverse financial time series with daily frequency.