Imitating Chemical Motors with Optimal Information Motors

Abstract

To induce transport, detailed balance must be broken. A common mechanism is to bias the dynamics with a thermodynamic fuel, such as chemical energy. An intriguing, alternative strategy is for a Maxwell demon to effect the bias using feedback. We demonstrate that these two different mechanisms lead to distinct thermodynamics by contrasting a chemical motor and information motor with identical dynamics. To clarify this difference, we study both models within one unified framework, highlighting the role of the interaction between the demon and the motor. This analysis elucidates the manner in which information is incorporated into a physical system. PACS numbers: 05.70. Ln, Information is physical [1]: it is stored in physical memories, and therefore the processing of information is constrained by the same thermodynamic limitations as any other physical process [2,3]. Remarkably, once information has been obtained, it can then serve as a thermodynamic resource similar to free energy. These observations have been the historic points of departure for investigations into the nature of information [2,3]. As a consequence, research has either focused on the manipulation of information in isolated memories, or simply on the engines that utilize that information. This division has been fruitful. Theoretical studies of memories, which have been verified by experiment [4], have led to insights into the thermodynamic costs of measurement [5] and erasure [6][7][8][9][10][11]; copying [12,13]; and proofreading [12]; while theoretical [14][15][16][17][18][19][20] and experimental [21,22] investigations of information (or feedback) motors have explored the fundamental limits to the conversion of information into work.Nevertheless, the thermodynamic qualities of information still need to be clarified, especially the mechanisms that allow a motor to exploit information to rectify thermal fluctuations. With this goal in mind, we highlight in this Letter the difference between information and a more traditional thermodynamic resource, the chemical free energy. We elaborate this distinction by comparing the entropy production rates of two motors with identical dynamics: a chemical motor powered by a chemical potential gradient and an information motor driven by feedback. For the chemical motor, we use traditional methods of thermodynamic analysis [23]. However, such methods cannot be applied to the information motor when the memory is left unspecified. Even still, a useful bound for its entropy production can be obtained from a refinement of the second law of thermodynamics for feedback and information, introduced by Sagawa and Ueda [11]. We demonstrate that, despite the identical dynamics, the information motor presents qualitatively different thermodynamics. We then trace this discrepancy to the features of the interaction between the ratchet and the memory by introducing a physical model of the information motor.Our motors are patterned on the Brownian ratchet [24] pictured in Fig. 1. The ratchet is composed of a particleFIG. 1. D...

Biochemical Machines for the Interconversion of Mutual Information and Work

“…Horowitz and Esposito showed that entropy production within a system X can be negative if X is coupled to a second system Y , and transitions in X decrease I(X; Y ) [18]. A third key result, essential to exorcising Maxwell's Demon [6,21], is that if X and Y are uncoupled from each other, yet coupled to heat baths at temperature T , then the total free energy is [22,23] HereF (X) = F eq (X) − kT x∈X p(x) ln(p eq (x)/p(x)) is the non-equilibrium free energy [20,23], with the tilde indicating the generalisation from the standard equilibrium free energy F eq (X). Systems X and Y could be two non-interacting spins, or two physically separated molecules.…”

Thermodynamics of Modularity: Structural Costs Beyond the Landauer Bound

“…The authors of Ref. [50] considered a situation where a chemical force replaces the role of information in driving the system out of equilibrium and extracting work. The authors of Ref.…”

Reversible feedback confinement

“…In the first part of the operation, the optimal feedback transforms the information contained in fluctuations into free energy but, by confining the system, it reduces the fluctuations exhausting the amount of information. Then, during work extraction, heat is allowed to enter the system which, in turn, develops new fluctuations that can be exploited in the next cycle of operation [4,[37][38][39][40]. * * * This work has been supported by grants ENFASIS (FIS2011-22644) and TerMic (FIS2014-52486-R) from the Spanish Government.…”