A basic task of information processing is information transfer (flow). Here
we study a pair of Brownian particles each coupled to a thermal bath at
temperature T1​ and T2​, respectively. The information flow in such a
system is defined via the time-shifted mutual information. The information flow
nullifies at equilibrium, and its efficiency is defined as the ratio of flow
over the total entropy production in the system. For a stationary state the
information flows from higher to lower temperatures, and its the efficiency is
bound from above by ∣T1​−T2​∣max[T1​,T2​]​. This upper bound is
imposed by the second law and it quantifies the thermodynamic cost for
information flow in the present class of systems. It can be reached in the
adiabatic situation, where the particles have widely different characteristic
times. The efficiency of heat flow|defined as the heat flow over the total
amount of dissipated heat|is limited from above by the same factor. There is a
complementarity between heat- and information-flow: the setup which is most
efficient for the former is the least efficient for the latter and {\it vice
versa}. The above bound for the efficiency can be [transiently] overcome in
certain non-stationary situations, but the efficiency is still limited from
above. We study yet another measure of information-processing [transfer
entropy] proposed in literature. Though this measure does not require any
thermodynamic cost, the information flow and transfer entropy are shown to be
intimately related for stationary states.Comment: 19 pages, 1 figur