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<italic>Adaptive</italic> controllers and signal processors play a key role in dealing with parameter uncertainties. This paper proposes an adaptive and new <italic>information theoretic</italic> algorithm for secure and optimal source-coding. We optimise the volume of the achievable <italic>rate-distortion-equivocation region</italic> by the private Helen’s rate (HR), defining a stochastic mean-field game (MFG). The aforementioned stochasticity deals with the additional uncoded side-information (SI) at the encoder-decoder, or even possibly-decoded SI at the eavesdropper (Eve). The stochastic partial derivative equations (SPDEs), namely the Hamilton-Jacobi-Bellman (HJB) and the Fokker-Planck-Kolmogorov (FPK) are presented, being solved by a discretised Lagrangian. We explore the <italic>Information-flow</italic> over the resultant <italic>Riemann-Sphere</italic> and our proposed SMFG’s stability from a many-body-theoretic perspective. We also show that while the equivocation (uncertainty) rate is <inline-formula> <tex-math notation="LaTeX">$\Delta \le min \{\mathcal {H}(\mathcal {X}),\mathcal {R}_{h} \}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\mathcal {I}(\mathcal {Y};\mathcal {Z}|\mathcal {W})$ </tex-math></inline-formula> which is upper-bounded to <inline-formula> <tex-math notation="LaTeX">$min\{ \mathcal {I}(\mathcal {X};\mathcal {Y}),\mathcal {I}(\mathcal {Y};\mathcal {Z}|\mathcal {W}) \}$ </tex-math></inline-formula>, versus <inline-formula> <tex-math notation="LaTeX">$\mathcal {I}(\mathcal {X};\mathcal {Z}|\mathcal {W})$ </tex-math></inline-formula> theoretically converges to the <italic>information-Bottleneck-bound</italic> <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}(\mathcal {X})$ </tex-math></inline-formula>. Simulation results also show an out-performance of our scheme over the existing work, proving the SMFG’s stability and an adequate distance to <italic>Pareto-Optimal sets</italic>. Our generic solution covers a comprehensive field of studies determining <italic>smooth non-linearity</italic>.

A Novel & Stable Stochastic-Mean-Field-Game for Lossy Source-Coding Paradigms: A Many-Body-Theoretic Perspective