Maximum Entropy Production Principle for Stock Returns

In our previous studies we have investigated the structural complexity of time series describing stock returns on New York's and Warsaw's stock exchanges, by employing two estimators of Shannon's entropy rate based on Lempel-Ziv and Context Tree Weighting algorithms, which were originally used for data compression. Such structural complexity of the time series describing logarithmic stock returns can be used as a measure of the inherent (model-free) predictability of the underlying price formation processes, testing the Efficient-Market Hypothesis in practice. We have also correlated the estimated predictability with the profitability of standard trading algorithms, and found that these do not use the structure inherent in the stock returns to any significant degree. To find a way to use the structural complexity of the stock returns for the purpose of predictions we propose the Maximum Entropy Production Principle as applied to stock returns, and test it on the two mentioned markets, inquiring into whether it is possible to enhance prediction of stock returns based on the structural complexity of these and the mentioned principle.Comment: 14 pages, 5 figure

Weak Scale From the Maximum Entropy Principle

The theory of multiverse and wormholes suggests that the parameters of the Standard Model are fixed in such a way that the radiation of the $S^{3}$ universe at the final stage $S_{rad}$ becomes maximum, which we call the maximum entropy principle. Although it is difficult to confirm this principle generally, for a few parameters of the Standard Model, we can check whether $S_{rad}$ actually becomes maximum at the observed values. In this paper, we regard $S_{rad}$ at the final stage as a function of the weak scale ( the Higgs expectation value ) $v_{h}$, and show that it becomes maximum around $v_{h}={\cal{O}}(300\text{GeV})$ when the dimensionless couplings in the Standard Model, that is, the Higgs self coupling, the gauge couplings, and the Yukawa couplings are fixed. Roughly speaking, we find that the weak scale is given by \begin{equation} v_{h}\sim\frac{T_{BBN}^{2}}{M_{pl}y_{e}^{5}},\nonumber\end{equation} where $y_{e}$ is the Yukawa coupling of electron, $T_{BBN}$ is the temperature where the Big Bang Nucleosynthesis starts and $M_{pl}$ is the Planck mass.Comment: 21 pages, 10 figures; references added, version to appear in PTEP (v2