Thermodynamics of information

Abstract

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 objectivity of the second law: does it depend, for example, on what we know about the system? For over a century, much e ort has been devoted to incorporating information into thermodynamics and assessing the entropic and energetic costs of manipulating information. More recently, this historically theoretical pursuit has become relevant in practical situations where information is manipulated at small scales, such as in molecular and cell biology, artificial nano-devices or quantum computation. Here we give an introduction to a novel theoretical framework for the thermodynamics of information based on stochastic thermodynamics and fluctuation theorems, review some recent experimental results, and present an overview of the state of the art in the field. S oon after the discovery of the second law of thermodynamics, James Clerk Maxwell illustrated the probabilistic nature of the law with a gedanken experiment, now known as Maxwell's demon 1,2 . He argued that if an intelligent being-a demon-had information about the velocities and positions of the particles in a gas, then that demon could transfer the fast, hot particles from a cold reservoir to a hot one, in apparent violation of the second law 1,2 .Maxwell's demon revealed the relationship between entropy and information for the first time-demonstrating that, by using information, one can relax the restrictions imposed by the second law on the energy exchanged between a system and its surroundings. But formulations of the second law attributed to Rudolf Clausius, Lord Kelvin and Max Planck 3 make no mention of information. Reconciling these two pictures involves two separate tasks. First, we must refine the second law to incorporate information explicitly. And second, we must clarify the physical nature of information, so that it enters the second law not as an abstraction, but as a physical entity. In this way, information manipulations such as measurement, erasure, copying and feedback can be thought of as physical operations with thermodynamic costs.The first task was partially accomplished by Léo Szilárd, who devised a stylized version of Maxwell's demon. Szilárd's demon exploits one bit of information (the outcome of an unbiased yes/no measurement) to implement a cyclic process that extracts kT ln 2 of energy as work from a thermal reservoir at temperature T , where k is Boltzmann's constant 4 . This suggests a quantitative relationship between the information used by the demon and the extractable work from a single thermal reservoir.Efforts to address the second task have been many and varied 1,2 . Léon Brillouin quantified the cost of measurement in some specific situations; Marian Smoluchowski 5 and Richard Feynman 6 demonstrated that fluctuations prevent apparent second-law violations in autonomous demons; and Rolf Landauer, Charles Bennett and Oliver Penrose 7 prov...

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