Entropy in one paragraph
Shannon entropy is the expected amount of surprise in a random variable: the average number of bits needed to describe an outcome drawn from its distribution. A series whose returns are spread evenly over many outcomes has high entropy; you learn little from one observation about the next. A series whose returns cluster into a few consistent outcomes has low entropy; structure exists and can be described. To compute it on prices you bin returns (or a transformed quantity) into categories, estimate their probabilities over a window, and sum probability times log probability with a minus sign. The binning and the window are choices, and they matter.
Why variance is not enough
Volatility measures spread. Two markets can have identical realised volatility while one moves in a tight, repeating structure and the other moves at random. Variance cannot tell them apart; entropy can. Kurtosis adds information about fat tails but is a single moment, sensitive to a few extreme observations and silent about how those extremes arrive. Entropy describes the whole distribution's shape, and looked at cumulatively (as the distribution builds up across the range of outcomes) it reveals where the probability mass is concentrating before the extreme event itself appears.
Use one: filtering chart patterns for information content
Most pattern detectors find shapes that look good in hindsight. The paper Entropy-Assisted Quality Pattern Identification in Finance (Gupta, Gupta, Singh and Kais, Entropy 2025) adds a filter: a pattern only counts if the price moves that followed it were one-sided and low-entropy over the historical sample. An entropy-based measure stands in for information gain, so patterns that produced high one-sided movement while keeping low local entropy are treated as more informative about future direction. The result is fewer, more trustworthy, non-overlapping patterns, each with a consistency score rather than a hit count.
Use two: seeing tail risk build in the cumulative entropic spectrum
The paper Signatures of Extreme Events in Cumulative Entropic Spectrum (Drzazga-Szczęśniak and co-authors, Entropy 2025) identifies the cumulative effect of a random variable's empirical distribution as a factor that amplifies the occurrence of extreme events. It introduces an information measure built on Shannon entropy for joint probabilities and tests it on market data around three extreme events: the Brexit referendum result, the COVID-19 Black Monday and the start of the Russian invasion of Ukraine. The cumulative measure shows distinctive signatures of each, even when the data are relatively noisy. On a desk, that becomes a regime warning that does not depend on variance alone, because the measure moves as the distribution's shape shifts.
Use three: regime detection
Combining entropy with realised volatility gives a two-dimensional picture of a market: quiet and structured, quiet and random, loud and structured, loud and random. Transitions between those quadrants are regime changes, and strategies that work in one quadrant often fail in another. Tracking the pair over rolling windows, and alerting on quadrant changes rather than on levels, is a practical way to use the measure without over-fitting it.
Use four: reading markets under concentrated policy news
Entropic signatures of market response under concentrated policy communication (Drzazga-Szczęśniak and co-authors, The European Physical Journal Plus, 2026) applies the same tools to the first 100 days of Donald Trump's second presidential term, across major stock indices in the Americas, Europe, and Asia and Oceania. Standard deviation and entropy decoupled over that period, which the authors read as entropy reflecting the diversity of outcomes rather than only their amplitude, and a sliding-window cumulative entropy rose during regional episodes with high information density. For a desk, the takeaway is that entropy adds a second axis to volatility when news arrives in dense bursts.
How to use it on a desk without fooling yourself
- Use it as a filter and a warning, never as a direction. Entropy says where information is, not which way price goes.
- Fix the binning and the window before you look at results, and keep them fixed. Changing them after the fact is curve fitting.
- Mind the sample size: entropy estimates on short windows are biased downwards. Compare like with like.
- Expect non-stationarity. A structure that held for a year can stop; the measure will tell you when the structure fades, which is the point.
- Log the score next to every alert so a reviewer can see what the tool saw.
Where this runs
The two Entropy papers run inside SignalDesk. Its pattern-recognition tools apply the entropy filter when ranking setups, which is why its pattern alerts carry a consistency score rather than a hit count. Its volatility-regime and tail-risk tools use cumulative entropic measures alongside realised volatility, so regime warnings do not depend on variance alone. The research page explains both papers in plain terms and links to the full texts.
Sources and further reading
- Entropy-Assisted Quality Pattern Identification in Finance, Entropy 27(4):430, 2025
- Signatures of Extreme Events in Cumulative Entropic Spectrum, Entropy 27(4):410, 2025
- Entropic signatures of market response under concentrated policy communication, The European Physical Journal Plus 141(8):955, 2026
- C. E. Shannon, A Mathematical Theory of Communication, 1948
This guide is engineering and product guidance from EntropyX Labs, a technology provider. It is not legal, regulatory or investment advice.