Energy transmission in quantum field theory requires information

The interface between different quantum field theories is an important concept that arises in a variety of problems in particle physics and condensed matter physics. However, it has been difficult to calculate the transmission rates of energy and information across interfaces.

Hirosi Ooguri, Professor at the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI) at the University of Tokyo and Fred Kavli Professor at the California Institute of Technology, together with his collaborators, Associate Professor Yuya Kusuki at Kyushu University, and Professor Andreas Karch and graduate students Hao-Yu Sun and Mianqi Wang at the University of Texas, Austin, showed that for theories in two dimensions with scale invariance there are simple and universal inequalities between three quantities: Energy transfer rate, Information transfer rate, and the size of Hilbert space (measured by the rate of increase of the number of states at high energy). Namely,

[ energy transmittance ] ≤ [ information transmittance] ≤ [ size of the Hilbert space ].

These inequalities imply that, in order to transmit energy, information must also be transmitted, and both require a sufficient number of states. They also showed that no stronger inequality is possible.

Both energy and information transmissions are important quantities, but they are difficult to calculate, and no relationship between them was known. By showing the inequality between these quantities, this paper sheds new light on this important but difficult problem.