Phase transitions in optimal strategies for betting

Kelly's criterion is a betting strategy that maximizes the long term growth rate, but which is known to be risky. Here, we find optimal betting strategies that gives the highest capital growth rate while keeping a certain low value of risky fluctuations. We then analyze the trade-off between the average and the fluctuations of the growth rate, in models of horse races, first for two horses then for an arbitrary number of horses, and for uncorrelated or correlated races. We find an analog of a phase transition with a coexistence between two optimal strategies, where one has risk and the other one does not. The above trade-off is also embodied in a general bound on the average growth rate, similar to thermodynamic uncertainty relations. We also prove mathematically the absence of other phase transitions between Kelly's point and the risk free strategy.Comment: 23 pages, 5 figure

Closed-loop control strategy with improved current for a flashing ratchet

We show how to switch on and off the ratchet potential of a collective Brownian motor, depending only on the position of the particles, in order to attain a current higher than or at least equal to that induced by any periodic flashing. Maximization of instant velocity turns out to be the optimal protocol for one particle but is nevertheless defeated by a periodic switching when a sufficiently large ensemble of particles is considered. The protocol presented in this article, although not the optimal one, yields approximately the same current as the optimal protocol for one particle and as the optimal periodic switching for an infinite number of them.Comment: 4 pages, 4 figure

Extracting work optimally with imprecise measurements

Measurement and feedback allows an external agent to extract work from a system in contact with a single thermal bath. The maximum amount of work that can be extracted in a single measurement and the corresponding feedback loop is given by the information acquired via the measurement, a result that manifests the close relation between information theory and stochastic thermodynamics. In this paper we show how to reversibly confine a Brownian particle in an optical tweezer potential and then extract the corresponding increase of the free energy as work. By repeatedly tracking the position of the particle and modifying the potential accordingly, we can extract work optimally even with a high degree of inaccuracy in the measurements.Comment: 13 pages, 6 figures. Published in Entropy (open access

Optimal strategies in collective Parrondo games

We present a modification of the so-called Parrondo's paradox where one is allowed to choose in each turn the game that a large number of individuals play. It turns out that, by choosing the game which gives the highest average earnings at each step, one ends up with systematic loses, whereas a periodic or random sequence of choices yields a steadily increase of the capital. An explanation of this behavior is given by noting that the short-range maximization of the returns is "killing the goose that laid the golden eggs". A continuous model displaying similar features is analyzed using dynamic programming techniques from control theory.Comment: 4 pages, 6 figures, revised version in published for

Measuring the Energy Efficiency of Evaporative Systems through a New Index - EvaCOP

Evaporative systems are probably the oldest technology for thermal comfort. However, they are still an essential technology in the food industry, environments for thermal comfort, and even for cooling data centers. Standards have been improved to compare the energy efficiency of this type of equipment. Using AHRI concepts with temperature data from the 29 most populous cities in the world, an EvaCOP index was created from temperatures that are easier to simulate than current parameters. The index parameters were tested in a laboratory located in Curitiba (Brazil). EvaCOP values of 45.58 and 25.77 W/W were found in the calculation in two different simulated equipment and compared with the compression cycle systems that in the most efficient machines is around 6.29 W/W.info:eu-repo/semantics/publishedVersio