Temporal Membranes: Delay-Induced Self-Retention Without Clocks or Memory Substrates

Area of Science:

• Theoretical Biology
• Complex Systems
• Origin of Life Studies

Background:

• Living systems require organization despite component fluctuations.
• Persistence of organization has both spatial and temporal dimensions.
• Existing origin-of-life theories primarily focus on spatial compartmentalization.

Purpose of the Study:

• To investigate if dissipative systems with delayed feedback can achieve temporal self-retention.
• To determine if memory of past states can exist without explicit clocks or memory variables.
• To explore the minimal conditions for temporal organization in artificial life.

Main Methods:

• Studied a minimal stochastic delay equation with inhibitory feedback.
• Quantified temporal self-retention by comparing autocorrelation decay time and dissipative timescale.
• Analyzed the transition across feedback strengths and scaling parameters.
• Used mutual information to confirm persistent state dependence.

Main Results:

• Temporal self-retention was observed, with an index crossing unity at τ ≈ 1.918.
• The regime persisted up to τ = 30.0 under default parameters.
• The transition occurred between feedback strengths β = 1.0-3.5.
• Mutual information confirmed dependence between present and delayed states in long-delay regimes.

Conclusions:

• A minimal delay-dissipative regime enables temporal organization beyond simple dissipation.
• This provides a proof of concept for temporal self-retention in artificial-life systems.
• Delayed feedback offers a mechanism for persistence in systems lacking explicit memory components.