Eidostates

(Terminology of Ben Schumacher)

• An Eidostate is information, at any scale, that the system can be CONDITIONED ON.
  • these could look like multi-scale TQFTs(boundary condition data)
  • perhaps ordinary TQFT’s already do the job, scale given by brane dimension?
  • Q: What is a relative formulation of this? What is eidostate relative to a fixed eidostate?
• Example Schumacher had in mind:
  • Landauer’s principle relates two types of information that a system can be conditioned on:
    • microstate conditions → heat (thermodynamics of system)
    • macrostate condition → memory (information theory of Maxwell demon)
  • In particular, Landauer’s principle says erasure of memory has thermodynamic cost
  • Eidostates $\{\text{microstate }x\}\otimes \{\text{memories of microstate }\alpha \}$
• This example motivates up to develop the quantum mechanics of eidostates.
• What if instead of a tensor as above, it’s a square-zero extension?