Analogy Between Gambling and Measurement-Based Work Extraction
Dror A. Vinkler, Haim H. Permuter, Neri Merhav

TL;DR
This paper draws an analogy between gambling and measurement-based work extraction in physics, extending the concepts to continuous variables and applying known methods to new problems involving energy, information, and memory effects.
Contribution
It introduces a novel analogy between gambling and information engines, enabling the transfer of methods and results between the two fields for various complex scenarios.
Findings
Extended gambling to continuous variables for financial applications.
Derived bounds for work extraction with unknown distributions.
Analyzed systems with energy loss and memory effects.
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…
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