Large work extraction and the Landauer limit in a continuous Maxwell demon

Abstract

The relation between entropy and information dates back to the classical Maxwell demon (MD) paradox [1], a thought experiment proposed in 1867 by J. C. Maxwell to violate the second law of thermodynamics. A variant of the classical MD is the Szilard engine proposed by L. Szilard in 1926 in which the demon observes, at a given time, the compartment occupied by a single molecule in a vessel and extracts work by operating a pulley device. Here we introduce the Continuous Maxwell Demon (CMD), a device capable of extracting arbitrarily large amounts of work per cycle by repeated measurements of the state of a system, and experimentally test it in single DNA hairpin pulling experiments. In the CMD the demon monitors the state of the DNA hairpin (folded or unfolded) by observing it at equally spaced time intervals but extracts work only when the molecule changes state. We demonstrate that the average maximum work per cycle that can be extracted by the CMD is limited by the information-content of the stored sequences, in agreement with the second law. Work extraction efficiency is found to be maximal in the large information-content limit where work extraction is fueled by rare events.In the Szilard engine the demon performs a one-bit measurement by observing, at a given time, the compartment ( ! , " ) occupied by a single molecule in a vessel of volume at temperature ( Figure 1A). The engine operates as follows: if the molecule occupies the left compartment ( ! ), a pulley device extracts the mean work ! = − # log ! where ! = ! / is the probability of the molecule observed in the left compartment; if it occupies the right compartment ( " = − ! ) the mean extracted work equals " = − # log " with " = 1 − ! . The average work per cycle that can be extracted in the classical MD equals $%&It is maximal for ! = " = 1/2, $%& '( ≤ ) = # log 2, ) being the Landauer limit. The resolution of the MD paradox, i.e. the fact that the engine can fully convert heat into work without any other change, came from the thermodynamics of data processing. Half a century ago it was shown that any irreversible logical operation, such as bit erasure, requires energy consumption typically on the order of k B T [2,3]. In 2 general, $%& '( equals the information-content I of one bit, = − ! log ! − " log " , restoring the second-law inequality,with the mean extracted work. Subsequent developments in experimental physics, often in combination with the theory of fluctuation theorems and information feedback [4][5][6][7][8] have provided experimental realizations and models of the MD that have tested Eq.2 and the Landauer limit [9][10][11][12][13][14][15][16].Here we introduce the continuous MD (CMD), a conceptually new information-toenergy conversion device that takes advantage of extracting work from rare events. The CMD is exemplified in Figure 1B. The demon monitors the motion of the molecule by observing it at equally spaced time intervals but extracts work only when the molecule changes compartment. A work-extraction cycle starts with an initial o...

Operational approach to quantum stochastic thermodynamics

“…By following the credo "information is physical" [67] and by treating the measurement and the system on an equal footing, no modification is necessary in our framework. We remark that our novel second law (91) was very recently already experimentally confirmed [107], see also the discussion in Ref. [82].…”

Stochastic thermodynamics with arbitrary interventions

“…To demonstrate the versatility of our approach, we consider the "continuous Maxwell demon" analysed in Ref. [24]. As in the standard Szilard engine we consider a single particle in a box of volume V , which we partition into two subvolumes V 0 + V 1 = V .…”

“…As in Ref. [24] we now assume perfect measurements such that S Sh (q) = 0 where q denotes the initial state of the ancilla (or memory) used to record the measurement result. Furthermore, we do not perform any work on the system by changing some protocol λ t , thus W tot = 0.…”

Work extraction, information-content and the Landauer bound in the continuous Maxwell Demon

“…This remains an interesting open question. The same issue arises in many other examples of multiple measurements under repeated feedback control [32][33][34][35] One of the most relevant results in [1] is that )*+ in Eq. (3), and more in general the information-content of the stored sequences for an arbitrary finite measurement time , saturates the average maximum extractable work (i.e.…”