# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### Thermodynamic efficiency of information and heat flow

##### External Resource

http://iopscience.iop.org/article/10.1088/1742-5468/2009/09/P09011/meta

(Publisher version)

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

There are no public fulltexts stored in PuRe

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Allahverdyan, A., Janzing, D., & Mahler, G. (2009). Thermodynamic efficiency of
information and heat flow.* Journal of Statistical Mechanics: Theory and Experiment,* *2009*(9): P09011, pp. 1-35. doi:10.1088/1742-5468/2009/09/P09011.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-C2F8-9

##### Abstract

A basic task of information processing is information transfer (flow).

P0

Here we study a pair of Brownian particles each coupled to a thermal bath

at temperatures T1 and T2 . 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 the flow to the total

entropy production in the system. For a stationary state the information flows

from higher to lower temperatures, and its efficiency is bounded from above by

(max[T1 , T2 ])/(|T1 amp;amp;amp;amp;amp;8722; 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 flowdefined

as the heat flow over the total amount of dissipated heatis limited from above

by the same factor. There is a complementarity between heat and information

flow: the set-up which is most efficient for the former is the least efficient for the

latter and 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 the 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.

P0

Here we study a pair of Brownian particles each coupled to a thermal bath

at temperatures T1 and T2 . 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 the flow to the total

entropy production in the system. For a stationary state the information flows

from higher to lower temperatures, and its efficiency is bounded from above by

(max[T1 , T2 ])/(|T1 amp;amp;amp;amp;amp;8722; 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 flowdefined

as the heat flow over the total amount of dissipated heatis limited from above

by the same factor. There is a complementarity between heat and information

flow: the set-up which is most efficient for the former is the least efficient for the

latter and 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 the 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.