My idea. Perhaps time can be expressed as

Where S is the entropy of entanglement of an arbitrary closed surface. r is the radius to the surface point. Integration over a closed surface.

This is very similar to the analogy. Time behaves as a potential, and entropy as a charge.

From this formula there are several possible consequences.

1.Bekenstein Hawking entropy for the event horizon. Light cone case

2.Gravitational time dilation. The case if matter inside a closed surface processes information at the quantum level according to the Margolis-Livitin theorem.

3.The formula is invariant under Lorentz transformations.

4.If this definition is substituted instead of time, then the interval acquires a different look, which probably indicates a different approach of the Minkowski pseudometric with a complex plane

Where is the squared length of Planck

Is such an interpretation possible? Sincerely, Kuyukov V.P.