# Thermodynamic efficiency of information and heat flow

@article{Allahverdyan2009ThermodynamicEO, title={Thermodynamic efficiency of information and heat flow}, author={Armen E. Allahverdyan and Dominik Janzing and G. Mahler}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2009}, volume={2009}, pages={09011} }

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 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…

## Figures from this paper

## 63 Citations

Stochastic thermodynamics of information processing: bipartite systems with feedback, signal inference and information storage

- Computer Science
- 2017

A framework for two continuously coupled systems, which includes information and refines the standard second law of thermodynamics of bipartite systems is developed, and a purely information theoretic quantity, which is called sensory capacity, is introduced.

Entropy balance and information processing in bipartite and nonbipartite composite systems

- Physics, Computer SciencePhysical Review E
- 2018

This paper constructs irreversibility measures in terms of extant information theoretic measures and relates them to the physical entropy productions that characterise the behaviour of single and composite systems in stochastic thermodynamics illustrating them with simple examples.

Thermodynamics with Continuous Information Flow

- Computer Science, Physics
- 2014

We provide a unified thermodynamic formalism describing information transfers in autonomous as well as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is…

Relations Between Work and Entropy Production for General Information-Driven, Finite-State Engines

- Mathematics, PhysicsArXiv
- 2016

Under very few assumptions, a simple derivation of a family of inequalities that relate the work extraction with the entropy production are proposed that are applicable to any finite number of cycles and for a general input information sequence (possibly correlated), which is not necessarily assumed even stationary.

The Liang-Kleeman Information Flow: Theory and Applications

- Computer ScienceEntropy
- 2013

Information flow/transfer provides a potential measure of the cause-effect relation between dynamical events, a relation usually hidden behind the correlation in a traditional sense.

Thermodynamic limits to information harvesting by sensory systems

- Mathematics, Biology
- 2014

An integral fluctuation theorem is derived for the entropy production and a measure of the information accumulated in the memory of a stochastic measurement device given an energy budget that shows that the amount of information is bounded by the average thermodynamic entropy produced by the process.

Thermodynamic aspects of information transfer in complex dynamical systems.

- Mathematics, MedicinePhysical review. E
- 2016

This work strengthens the Liang-Kleeman heuristic balance reasoning by showing its formal analogy with the recent Horowitz-Esposito thermodynamic balance arguments.

Information thermodynamics for interacting stochastic systems without bipartite structure

- Computer Science, PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2019

The generalization of information-theoretic measures, such as learning rates and transfer entropy rates, to this situation is non-trivial and also involves introducing several additional rates, and an important relation linking information theory and estimation theory is generalized.

Thermodynamics of information

- Physics
- 2015

By its very nature, the second law of thermodynamics is probabilistic, in that its formulation requires a probabilistic description of the state of a system. This raises questions about the…

Thermodynamic implications of non-reciprocity

- Physics
- 2020

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general…

## References

SHOWING 1-10 OF 106 REFERENCES

A rigorous formalism of information transfer between dynamical system components. II. Continuous flow

- Mathematics
- 2007

The transfer of information between dynamical system components is formalized with causality faithfully represented. In a continuous system with many components, information transfer is a mechanism…

METHODOLOGICAL NOTES: Maxwell demon and the correspondence between information and entropy

- Physics
- 1979

Thermodynamic models are discussed for various methods of introducing order in a system (for carrying out a control process). The concept of entropic efficiency is introduced as a measure of the…

Steady adiabatic state: its thermodynamics, entropy production, energy dissipation, and violation of onsager relations

- Physics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

A generalized statistical thermodynamics is constructed and a universal variational principle is proposed, which states that to leading order in the small ratio of the characteristic times, there exists a universal relation between them.

Thermodynamics of computing: Entropy of nonergodic systems.

- Mathematics, MedicineChaos
- 2001

It is shown that the erasing process, involving a transition from a nonergodic to an ergodic state, is irreversible and accompanied with k ln 2/bit of entropy generation, while the heat generation occurs in a writing process.

Thermodynamic models of information processes

- Computer Science
- 1975

A relation is established between physical entropy and quantity of information and these results are used to determine the energy cost of information transmission with allowance for the energy expenditures on decoding.

Fast and slow degrees of freedom coupling two different reservoirs.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

This work applied the formalism to a coupled system of ideal gases and also to an ideal gas interacting with a harmonic oscillator, finding that if the temperatures of the heat baths are not too close, the Onsager relations do not apply.

Breakdown of the Landauer bound for information erasure in the quantum regime.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

A quantum Brownian particle interacting with its thermal bath can either generate less heat or even absorb heat during an analogous squeezing process, due to entanglement with the bath, and this invalidates the Landauer bound in the quantum regime, and suggests that quantum carriers of information can be more efficient than assumed so far.

Maxwell's demon and the entropy cost of information

- Mathematics
- 1996

We present an analysis of Szilard's one-molecule Maxwell's demon, including a detailed entropy accounting, that suggests a general theory of the entropy cost of information. It is shown that the…

Examining structural dynamics using information flow

- Mathematics
- 2006

Abstract In this work, two different information-theoretic approaches are presented for exploring coupling in structural dynamics. Specifically, both the time delayed mutual information and the…

The thermodynamics of computation—a review

- Physics
- 1982

Computers may be thought of as engines for transforming free energy into waste heat and mathematical work. Existing electronic computers dissipate energy vastly in excess of the mean thermal…