It is a surprisingly powerful analogy: markets can look calm on the surface, then suddenly develop “financial storms” with bursts of volatility, correlated movements, and extreme events.

The key difference is that water molecules do not anticipate the future—traders do.

That makes markets more adaptive and unpredictable than ordinary fluid turbulence.

A simplified mathematical analogy is to compare a fluid’s velocity change over a time or distance interval,

Δv(τ)=v(t+τ)−v(t),
Δv(τ)=v(t+τ)−v(t),

with a stock’s return over a time interval,

r(τ)=ln⁡P(t+τ)−ln⁡P(t).
r(τ)=lnP(t+τ)−lnP(t).

Researchers then examine how the variability of these changes depends on the scale τ
τ, often using quantities such as

Sq(τ)=E[∣Δv(τ)∣q]
Sq​(τ)=E[∣Δv(τ)∣q]

for fluids and

Sq(τ)=E[∣r(τ)∣q]
Sq​(τ)=E[∣r(τ)∣q]

for markets.

The analogy is useful because both systems are complex, multiscale, nonlinear, and capable of sudden extreme events.

But it is not exact: a fluid follows physical conservation laws, whereas markets consist of adaptive human and algorithmic agents whose behavior changes in response to expectations, rules, news, and incentives.

https://arxiv.org/html/2508.20105v2