Thermodynamic efficiency of information and heat flow

TL;DR

This paper investigates the thermodynamic limits of information and heat flow between two coupled Brownian particles at different temperatures, revealing bounds imposed by the second law and a trade-off between heat and information transfer efficiencies.

Contribution

It introduces a thermodynamic efficiency bound for information flow in coupled systems and explores the relationship between heat and information transfer, including transient violations and transfer entropy.

Findings

Maximum information flow efficiency is bounded by temperature difference.

Heat flow efficiency shares the same upper bound as information flow.

A trade-off exists: systems optimized for heat transfer are less efficient for information transfer.

Abstract

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 $T_1$ and $T_2$, 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 $\frac{{\rm max}[T_1,T_2]}{|T_1-T_2|}$. 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.