  Signal transduction in living cells is vital to maintain life itself, where
information transfer in noisy environment plays a significant role. In a rather
different context, the recent intensive researches of "Maxwell's demon" - a
feedback controller that utilizes information of individual molecules - has led
to a unified theory of information and thermodynamics. Here we combine these
two streams of researches, and show that the second law of thermodynamics with
information reveals the fundamental limit of the robustness of signal
transduction against environmental fluctuations. Especially, we found that the
degree of robustness is quantitatively characterized by an informational
quantity called transfer entropy. Our information-thermodynamic approach is
applicable to biological communication inside cells, in which there is no
explicit channel coding in contrast to artificial communication. Our result
would open up a novel biophysical approach to understand information processing
in living systems on the basis of the fundamental information-thermodynamics
link.
