🧩 Flows vs. States in Market Microstructure

Market data fundamentally comes in two ontologically distinct categories:
instantaneous states and aggregated flows.

Category	Examples	Nature	Mathematical Form
State variables	Price, Open Interest (OI), Funding Rate, Inventory, Liquidity Depth	Snapshot at a given instant — represents how much exists right now	$S(t)$
Flow / Activity variables	Volume, Turnover, Transaction Count, Notional Traded	Cumulative or rate-of-change over an interval — represents how much changed during Δt	$\int_{t-\Delta t}^{t} f(\tau) \, d\tau$

A state variable is like a photo;
a flow variable is like a video segment.

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⚙️ Reconciling the Two

Because they live in different dimensions (one per time, one at a time), they can’t be directly compared without transformation.

1. Convert a Flow to a Rate

$$\text{Intensity}(t) = \frac{\text{Volume}(t, t+\Delta t)}{\Delta t}$$

This expresses how active the market is per unit time — e.g., trades per second.

2. Convert a State to a Flow Proxy

$$\dot{OI}(t) = \frac{d\,OI}{dt}$$

This measures the rate of position creation/closure — an “OI flow.”
Now both terms live in rate-space and can be compared:

$$\eta(t) = \frac{|\Delta OI(t)|}{\text{Volume}(t)}$$

This fraction represents the share of traded volume that results in new exposure rather than position rotation.

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🧮 Derived Ratios

Metric	Formula	Interpretation
Turnover Rate	$R(t) = \frac{V(t)}{OI(t)}$	How many times the open book “trades” per chosen time unit.
Position Formation Ratio	$\eta(t) = \frac{\Delta OI(t)}{V(t)}$	What share of volume created or closed positions.

Both can be expressed per time window (1h, 1d, etc.) for consistency.

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🧭 Philosophical Framing

• Stocks (States): how much exists — the system’s potential energy.
• Flows: how much moves — the system’s kinetic energy.

When large flows meet large stocks, markets enter high-stress regimes:
latent leverage meets realized trading activity.

Most dynamic indicators (funding, delta imbalance, volatility) emerge at this interface between stocks and flows.

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🧠 Key Takeaway

Volume is always an aggregation over time.
Open Interest is always an instantaneous measurement.

Confusing the two leads to misleading interpretations.
Recognizing their dimensional difference — and translating one into the other when needed — is the foundation for constructing meaningful stock-to-flow metrics in leveraged markets.