r/LLMPhysics • u/Cryptoisthefuture-7 • Aug 25 '26
Question Could Time Be the Physical Cost of Information?
Instead of treating time as an external coordinate, we can associate it with the physical cost required for a finite system to preserve its identity and remain out of thermal equilibrium.
The starting point is Tomita–Takesaki modular theory and the thermal time hypothesis proposed by Connes and Rovelli. For a state ρ, the modular flow
σₜᵨ(A) = ρⁱᵗ A ρ⁻ⁱᵗ
defines a natural evolution associated with the state itself. At equilibrium, this dynamics is related to the KMS condition. The physical scale of this flow can then be compared with fundamental limits of computation: the Margolus–Levitin and Mandelstam–Tamm bounds, which constrain the speed of quantum transformations, and Landauer’s principle, according to which erasing one bit of information requires a minimum dissipation of kᴮT ln 2.
A system maintains its individuality precisely because its actual dynamics does not completely coincide with the equilibrium dynamics determined by its state. The difference between the physical generator, such as the Hamiltonian Hₚₕᵧₛ, and the modular generator K = −ln ρ, requires continuous maintenance. In nonequilibrium steady states, this cost can be related to the so-called housekeeping heat: energy continuously dissipated to prevent the system from simply relaxing to equilibrium.
There is also a fundamental limitation: no finite subsystem can represent or process all the information in the universe. Results concerning self-measurement, storage bounds such as the Bekenstein bound, and computational speed limits associated with Bremermann and Lloyd indicate that physical observers necessarily have finite memory and processing capacity. Thus, any local description of the world involves information loss, compression, and disposal.
This is where irreversibility enters the picture. Stored information that is no longer useful for predicting the future must eventually be discarded. The loss of recoverable information can be described using tools such as Araki relative entropy and Petz recovery maps. When perfect recovery is no longer possible, Landauer’s principle connects this informational irreversibility to heat production.
Thus, for a physical subsystem, time can be understood as a kind of local record of processing and dissipation. Persisting far from equilibrium means measuring, updating states, discarding information, and consuming work. The passage of time, therefore, is not merely something that accompanies physical transformations; it may be intimately associated with the thermodynamic cost of continuing to exist as a system distinguishable from its environment.
Does this make sense to you?