Temporal Duality in Non-Equilibrium Materials: Reversible and Irreversible Time Regimes in Viscoelastic and Aging Systems

Non-equilibrium materials often exhibit a complex interplay between reversible elastic responses and irreversible processes such as viscous dissipation, structural relaxation, and aging. Classical constitutive models typically describe these behaviors using a single temporal variable, which can obscure the distinct physical mechanisms involved and require empirical memory kernels to account for history dependence. In this work, we address this limitation by introducing a temporal duality framework in which material behavior is governed by two coupled time regimes: a reversible time coordinate associated with elastic, time-symmetric dynamics, and an irreversible time coordinate associated with dissipative, aging, and time-asymmetric evolution. This dual-time formulation enables a unified description of viscoelasticity, memory effects, and aging, while providing structural clarity to the thermodynamic origins of irreversibility. Classical models are recovered as limiting cases, and illustrative examples show how the framework can reproduce stress–relaxation and aging behaviors commonly observed in polymers and disordered materials. This approach offers a new pathway for interpreting and modeling time-dependent behavior in non-equilibrium systems without relying on phenomenological assumptions.