Research · Entropy 2025 · EPJ Plus 2026

How much information is actually in a market?

That question started EntropyX Labs. Our founder and CEO, Shivam Gupta, has co-authored three peer-reviewed answers: two in Entropy (2025), on finding patterns that carry information and on seeing tail risk build up, and one in The European Physical Journal Plus (2026), on how stock markets respond to concentrated policy news. The two Entropy methods run inside SignalDesk today. This page explains each in plain terms and links to the papers.

Last updated 2026-11-13 · About the founder
Peer-reviewed The European Physical Journal Plus, Vol. 141, Issue 8, Article 955 · 2026

Entropic signatures of market response under concentrated policy communication

In plain terms When policy news arrives in a dense burst, volatility and entropy tell different stories. The paper finds the two decouple: entropy is not just a proxy for the size of moves but reflects how many different outcomes the market is producing, and its cumulative form rises during regional episodes with high information density.

Abstract A first look, rooted in information theory, at the first 100 days of Donald Trump's second presidential term (20 January to 30 April 2025) as a case of concentrated policy communication, analysing major stock indices across the Americas, Europe, and Asia and Oceania. The approach jointly examines dispersion (standard deviation) and information complexity (entropy), and uses a sliding-window cumulative entropy to localise extreme events.

authors
E. A. Drzazga-Szczęśniak, R. Gupta, A. Z. Kaczmarek, J. T. Gnyp, M. W. Jarosik, R. Waligóra, M. Kielak, S. Gupta, A. Gurzyńska, J. Gil, P. Szczepanik, J. Kielak, D. Szczęśniak
doi
10.1140/epjp/s13360-026-08130-5
Read the paper
Peer-reviewed Entropy (MDPI), Vol. 27, Issue 4, Article 430 · 2025

Entropy-Assisted Quality Pattern Identification in Finance

In plain terms Most pattern detectors find shapes that look good in hindsight. This paper adds a filter: a pattern only counts if the price moves that followed it were consistent (low entropy) and one-sided. The result is fewer, more trustworthy patterns.

Abstract An entropy-assisted framework for identifying high-quality, non-overlapping patterns that exhibit consistent behaviour over time. The approach uses an entropy-based measure as a proxy for information gain: patterns that produce high one-sided movements in historical data yet retain low local entropy are treated as more informative signals of future market direction.

In SignalDesk

SignalDesk's pattern-recognition tools apply this entropy filter when ranking setups, which is why its pattern alerts carry a consistency score rather than a hit count.

authors
R. Gupta, S. Gupta, J. Singh, S. Kais
doi
10.3390/e27040430
Read the paper See it in SignalDesk
Peer-reviewed Entropy (MDPI), Vol. 27, Issue 4, Article 410 · 2025

Signatures of Extreme Events in Cumulative Entropic Spectrum

In plain terms Extreme moves leave a fingerprint in how a series' probability distribution accumulates. Tested on markets around the Brexit referendum result, the COVID-19 Black Monday and the start of the Russian invasion of Ukraine, the cumulative entropy measure showed distinctive signatures of each event, even in noisy data, and the authors argue it can become a new class of indicator.

Abstract The cumulative effect of the empirical probability distribution of a random variable is identified as a factor that amplifies the occurrence of extreme events in datasets. A corresponding information measure, drawing on Shannon entropy for joint probabilities, is validated on market data around extreme events; the cumulative measure shows distinctive signatures of such events, even when the data are relatively noisy.

In SignalDesk

The volatility-regime and tail-risk tools in SignalDesk use cumulative entropic measures alongside realised volatility, so regime warnings do not depend on variance alone.

authors
E. A. Drzazga-Szczęśniak, A. Z. Kaczmarek, M. Kielak, S. Gupta, J. T. Gnyp, K. Pluta, Z. Bąk, P. Szczepanik, D. Szczęśniak
doi
10.3390/e27040410
Read the paper See it in SignalDesk
Research · Quantum

The “X” in EntropyX isn't marketing.

We started as a research group obsessed with one question: how much information is actually in a market? That question chose what we build, what we optimise, and where the next decade of edge lives.

|0⟩|ψ⟩|1⟩H · ƒ(x)

Quantum-inspired optimisation

Variational and annealing-style solvers tuned for portfolio rebalancing, routing and combinatorial pricing — running today on classical hardware, ready for quantum back-ends.

QAOA VQE annealing

Information theory in finance

Entropy as a market signal. Our published work shows local entropy plus directional movement isolates patterns conventional moment statistics miss.

entropy patterns MDPI

Hybrid classical/quantum stack

Production services where quantum subroutines slot in as drop-in replacements when meaningful. No rewrites, no lock-in.

hybrid runtime service mesh

From paper to production

Every research artefact ships with a productionisation plan. We measure ourselves on what reaches a customer.

paper → prod evals

Cross-asset signal graphs

Information-theoretic dependency graphs across FX, equities, commodities and crypto — capturing lead/lag relationships that linear correlation matrices erase.

transfer entropy lead/lag regime

Robustness & uncertainty

Every model ships with calibrated confidence intervals, drift monitors and adversarial stress tests. Forecasts come with conviction, not just point estimates.

calibration drift stress-tested
Selected publications · 2025–2026
Peer-reviewed · 2026 · Springer

Entropic signatures of market response under concentrated policy communication

A first look, rooted in information theory, at the first 100 days of Donald Trump's second presidential term (20 January to 30 April 2025) as a case of concentrated policy communication, analysing major stock indices across the Americas, Europe, and Asia and Oceania. The approach jointly examines dispersion (standard deviation) and information complexity (entropy), and uses a sliding-window cumulative entropy to localise extreme events.

authors E. A. Drzazga-Szczęśniak, R. Gupta, A. Z. Kaczmarek, J. T. Gnyp, M. W. Jarosik, R. Waligóra, M. Kielak, S. Gupta, A. Gurzyńska, J. Gil, P. Szczepanik, J. Kielak, D. Szczęśniak
venue The European Physical Journal Plus, Vol. 141, Issue 8, Article 955
doi 10.1140/epjp/s13360-026-08130-5
information theory entropy policy communication stock indices extreme events
Peer-reviewed · 2025 · MDPI

Entropy-Assisted Quality Pattern Identification in Finance

An entropy-assisted framework for identifying high-quality, non-overlapping patterns that exhibit consistent behaviour over time. The approach uses an entropy-based measure as a proxy for information gain: patterns that produce high one-sided movements in historical data yet retain low local entropy are treated as more informative signals of future market direction.

authors R. Gupta, S. Gupta, J. Singh, S. Kais
venue Entropy (MDPI), Vol. 27, Issue 4, Article 430
doi 10.3390/e27040430
information theory pattern recognition financial markets predictive signals
Peer-reviewed · 2025 · MDPI

Signatures of Extreme Events in Cumulative Entropic Spectrum

The cumulative effect of the empirical probability distribution of a random variable is identified as a factor that amplifies the occurrence of extreme events in datasets. A corresponding information measure, drawing on Shannon entropy for joint probabilities, is validated on market data around extreme events; the cumulative measure shows distinctive signatures of such events, even when the data are relatively noisy.

authors E. A. Drzazga-Szczęśniak, A. Z. Kaczmarek, M. Kielak, S. Gupta, J. T. Gnyp, K. Pluta, Z. Bąk, P. Szczepanik, D. Szczęśniak
venue Entropy (MDPI), Vol. 27, Issue 4, Article 410
doi 10.3390/e27040410
extreme events tail risk cumulative entropy stochastic systems
FAQ

Research questions

What is entropy-based pattern identification?

A way of filtering chart patterns by how consistent the price behaviour after them was. Patterns followed by one-sided moves with low local entropy are treated as more informative; patterns with noisy, mixed outcomes are discarded. It was published in Entropy (MDPI) in 2025.

What is the cumulative entropic spectrum?

An entropy measure computed cumulatively over a series' empirical distribution rather than at a single point. In the 2025 paper it showed distinctive signatures around three extreme market events, even in relatively noisy data, which the authors argue can support new indicators of extreme events.

What does entropy show when policy news is concentrated?

The 2026 paper in The European Physical Journal Plus studied the first 100 days of Donald Trump's second term across major stock indices. Entropy and standard deviation decoupled, so entropy was not just a proxy for the size of moves, and a sliding-window cumulative entropy rose during regional episodes with high information density.

Can entropy measure how much information is in a market?

It can measure how predictable a series is over a window, which is a practical proxy. Low local entropy with directional movement indicates structure; high entropy indicates noise. SignalDesk uses that distinction to rank patterns and warn about regimes.

Where is this used in your products?

In SignalDesk: the pattern-recognition tools apply the entropy filter when ranking setups, and the volatility-regime tools use cumulative entropic measures alongside realised volatility.

Do you take research collaborations?

Yes, with academic groups and with clients who have data problems worth publishing. Write to sales@entropyxlabs.com with the subject 'Research'.

Have a data problem worth publishing?

We collaborate with academic groups and with clients whose questions deserve a paper, and we productise what holds up.

Write to us sales@entropyxlabs.com