Thermodynamics with Continuous Information Flow

Abstract

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 continuously generated in an auxiliary system and then transferred to a relevant system that can utilize it to fuel otherwise impossible processes. Indeed, while the joint system satisfies the second law, the entropy balance for the relevant system is modified by an information term related to the mutual information rate between the two systems. We show that many important results previously derived for nonautonomous Maxwell demons can be recovered from our formalism and use a cycle decomposition to analyze the continuous information flow in autonomous systems operating at a steady state. A model system is used to illustrate our findings.

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Plain Language Summary

Information is often perceived as an immaterial entity. However, since the birth of statistical physics, it has been argued, based on thought experiments by the likes of Maxwell, that there are physical thermodynamic implications to information manipulation. In recent years, these thought experiments have started to become reality: Technological advancements make it possible to manipulate small fluctuating systems on thermal energy scales. In parallel, significant theoretical progress has been made in the thermodynamic description of information processing. However, a unified framework incorporating both nonautonomous systems, i.e., systems manipulated by an external agent that controls macroscopic parameters, and autonomous systems powered by a constant supply of energy, has been lacking until now. We provide such a unified framework delineating how information collected by one system continuously flows to another where it is exploited as a useful resource.

When two systems interact, autonomously or nonautuonomously, they exchange not only energy but also information. Our central result demonstrates how the second law of thermodynamics is modified in the presence of this information. We show that one system may act as a thermodynamic machine, burning fuel to produce information that flows to the second system, where the fuel can be consumed to perform an otherwise impossible task. When the pair of systems is considered as a whole, the traditional second law of thermodynamics is recovered, thereby consistently accounting for the cost of information processing. From this framework, we reproduce earlier results on Maxwell demons—theoretical descriptions of how to violate the second law of thermodynamics—and identify information flow in autonomous systems.

We expect that this new method of analysis will have applications beyond statistical physics in engineering and biology, and it may reveal how devices or organisms gather information about their world in order to optimize their energy consumption.