Jarzynski-type equalities in gambling: role of information in capital growth
arXiv:1505.06216 · doi:10.1007/s10955-015-1348-0
Abstract
We study the capital growth in gambling with (and without) side information and memory effects. We derive several equalities for gambling, which are of similar form to the Jarzynski equality and its extension to systems with feedback controls. Those relations provide us with new measures to quantify the effects of information on the statistics of capital growth in gambling. We discuss the implications of the equalities and show that they reproduce the known upper bounds of average capital growth rates.
32 pages, no figure; ver2: version to appear in Journal of Statistical Physics
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- Stochastic thermodynamics of interacting degrees of freedom: Fluctuation theorems for detached path probabilities
- A Generalization of the Classical Kelly Betting Formula to the Case of Temporal Correlation
- Information thermodynamics of financial markets: the Glosten-Milgrom model
- Sex as information processing: optimality and evolution