Empirical Inference Article 2009

Thermodynamic efficiency of information and heat flow

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 − 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 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.

Author(s): Allahverdyan, AE. and Janzing, D. and Mahler, G.
Journal: Journal of Statistical Mechanics: Theory and Experiment
Volume: 2009
Number (issue): 09
Pages: P09011
Year: 2009
Month: September
Day: 0
Bibtex Type: Article (article)
DOI: 10.1088/1742-5468/2009/09/P09011
Electronic Archiving: grant_archive
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik
Links:

BibTex

@article{6216,
  title = {Thermodynamic efficiency of information and heat flow},
  journal = {Journal  of Statistical Mechanics: Theory and  Experiment},
  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 − 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 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.},
  volume = {2009},
  number = {09},
  pages = {P09011},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  month = sep,
  year = {2009},
  slug = {6216},
  author = {Allahverdyan, AE. and Janzing, D. and Mahler, G.},
  month_numeric = {9}
}