Maxwell’s Refrigerator: An Exactly Solvable Model

Mandal, Dibyendu; Quan, H. T.; Jarzynski, Christopher

doi:10.1103/physrevlett.111.030602

Cited by 144 publications

(226 citation statements)

References 47 publications

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“…It was shown that, for a system with finite memory, the cost of bits erasure nullifies any gain from such a demon [2][3][4][5][6][7]. However, it was not until recently that Sagawa and Ueda reached a general upper bound on the amount of work that can be extracted [8,9], which was also demonstrated experimentally [10,11].…”

Section: Introductionmentioning

confidence: 93%

“…The equations defining both problems, (2) and (10), are the same if one renames b X|Y as v f and o X as 1/P X . The analogy also holds for the optimal strategy in both problems, presented in (4) and (11), and the maximum gain, presented in (6) and (12), where log S n is renamed W n /k B T . Analogous to the way bits of side information are converted into wealth in gambling, bits of measurements are converted into work in the Szilard Engine.…”

Section: Analogymentioning

confidence: 99%

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Analogy between gambling and measurement-based work extraction

2016

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Abstract. In information theory, one area of interest is gambling, where mutual information characterizes the maximal gain in wealth growth rate due to knowledge of side information; the betting strategy that achieves this maximum is named the Kelly strategy. In the field of physics, it was recently shown that mutual information can characterize the maximal amount of work that can be extracted from a single heat bath using measurement-based control protocols, i.e., using "information engines". However, to the best of our knowledge, no relation between gambling and information engines has been presented before. In this paper, we briefly review the two concepts and then demonstrate an analogy between gambling, where bits are converted into wealth, and information engines, where bits representing measurements are converted into energy. From this analogy follows an extension of gambling to the continuousvalued case, which is shown to be useful for investments in currency exchange rates or in the stock market using options. Moreover, the analogy enables us to use well-known methods and results from one field to solve problems in the other. We present three such cases: maximum work extraction when the probability distributions governing the system and measurements are unknown, work extraction when some energy is lost in each cycle, e.g., due to friction, and an analysis of systems with memory. In all three cases, the analogy enables us to use known results in order to obtain new ones.

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Section: Introductionmentioning

confidence: 93%

Section: Analogymentioning

confidence: 99%

Analogy between gambling and measurement-based work extraction

2016

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“…We believe that similar extensions can be offered also for the other variations of this model, that appear in [1], [2], [3], and [15], as mentioned.…”

Section: Introductionmentioning

confidence: 99%

“…It may also act as an eraser, which implements the opposite process of losing energy while erasing information, that is, decreasing the entropy. Several variations on this model, based on similar ideas, were offered in some subsequent works, e.g., [1], [2], [3], and [15].…”

Section: Introductionmentioning

confidence: 99%

“…A non-exhaustive list of recent works on the modern approach of incorporating informational ingredients in physical systems includes [1], [2], [3], [5], [6], [8], [9], [10], [11], [14], [15], [18], [20], [21], and [22]. In some of these works, the informational resources are available by means of measurement and feedback control (like in the Maxwell's demon and Szilard's engine) and other works are about physical systems that include, in addition to the traditional heat reservoir, also an information reservoir, which interacts with the system, but without any energy exchange.…”

Section: Introductionmentioning

confidence: 99%

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Sequence complexity and work extraction

Merhav

2015

J. Stat. Mech.

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Abstract. We consider a simplified version of a solvable model by Mandal and Jarzynski, which constructively demonstrates the interplay between work extraction and the increase of the Shannon entropy of an information reservoir which is in contact with a physical system. We extend Mandal and Jarzynski's main findings in several directions: First, we allow sequences of correlated bits rather than just independent bits. Secondly, at least for the case of binary information, we show that, in fact, the Shannon entropy is only one measure of complexity of the information that must increase in order for work to be extracted. The extracted work can also be upper bounded in terms of the increase in other quantities that measure complexity, like the predictability of future bits from past ones. Third, we provide an extension to the case of non-binary information (i.e., a larger alphabet), and finally, we extend the scope to the case where the incoming bits (before the interaction) form an individual sequence, rather than a random one. In this case, the entropy before the interaction can be replaced by the Lempel-Ziv (LZ) complexity of the incoming sequence, a fact that gives rise to an entropic meaning of the LZ complexity, not only in information theory, but also in physics.

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Entropy, Information and Energy Flows

Loos

2021

Stochastic Systems With Time Delay

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Maxwell’s Refrigerator: An Exactly Solvable Model

Cited by 144 publications

References 47 publications

Analogy between gambling and measurement-based work extraction

Analogy between gambling and measurement-based work extraction

Sequence complexity and work extraction

Entropy, Information and Energy Flows

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