Misanthropic entropy and renormalization as a communication channel
- Vigilant Cyber Systems, Mt Airy, NC 27030, USA
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
A central physical question is the extent to which infrared (IR) observations are sufficient to reconstruct a candidate ultraviolet (UV) completion. We recast this question as a problem of communication, with messages encoded in field configurations of the UV being transmitted to the IR degrees of freedom via a noisy channel specified by renormalization group (RG) flow, with noise generated by coarse graining/decimation. We present an explicit formulation of these considerations in terms of lattice field theory, where we show that the “misanthropic entropy” — the mutual information obtained from decimating neighbors — encodes the extent to which information is lost in marginalizing over/tracing out UV degrees of freedom. Our considerations apply both to statistical field theories as well as density matrix renormalization of quantum systems, where in the quantum case, the statistical field theory analysis amounts to a leading-order approximation. As a concrete example, we focus on the case of the 2D Ising model, where we show that the misanthropic entropy detects the onset of the phase transition at the Ising model critical point.
- Research Organization:
- Univ. of Pennsylvania, Philadelphia, PA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- SC0013528
- OSTI ID:
- 1980828
- Journal Information:
- International Journal of Modern Physics A, Vol. 37, Issue 16; ISSN 0217-751X
- Publisher:
- World Scientific
- Country of Publication:
- United States
- Language:
- English
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