Every river meeting the sea is performing the world's largest mixing experiment — and dissipating an enormous amount of free energy in the process. When freshwater (low entropy, ordered) merges with saltwater (high entropy, disordered), the Gibbs free energy of mixing is released as heat that warms the estuary by a few millikelvin. Tap that energy before it's lost, and you have a fully renewable, baseload power source.

The thermodynamic ceiling, set by van 't Hoff's equation for osmotic pressure, is about 2.2 MJ per cubic meter of freshwater mixed with seawater. That's roughly equivalent to letting the same cubic meter fall 224 meters — every river is essentially a giant invisible waterfall.

Back-of-envelope, Mississippi River edition:

• Mean discharge: 17,000 m³/s
• Theoretical power: 17,000 × 2.2 MJ = 37 GW continuous
• That's ~30 nuclear reactors flowing past New Orleans, day and night
• Globally: rivers dump 37,000 km³/yr to oceans → 2.6 TW of theoretical baseload — within a factor of 2 of all human electricity demand

Two ways to harvest it:

Pressure-retarded osmosis (PRO): Freshwater diffuses through a semipermeable membrane into pressurized seawater (~26 bar). The pressurized brine spins a hydroturbine. Statkraft built the world's first PRO plant in Norway in 2009 — and shut it down in 2014. Reason: power density. Their best membranes delivered ~1 W/m². At that rate, replacing the Mississippi's 37 GW of potential needs 37 billion m² of membrane — a sheet the size of Switzerland.

Reverse electrodialysis (RED): Alternating cation- and anion-selective membranes let salt ions move down their concentration gradient, generating an EMF directly. No high pressure, but the same fouling and density problems. State-of-the-art lab membranes hit ~6 W/m² with high-purity solutions; real estuarine water with sediment, microbes, and humic acid degrades that by 50–80%.

The engineering wall: To make salinity-gradient power competitive with offshore wind (~$80/MWh), membranes need to reach ~10 W/m² sustained at $20/m² with 10-year fouling resistance. Today: ~3 W/m² and $50/m². The gap is closing — graphene-oxide and boron-nitride composites have shown 20+ W/m² in lab cells using ultra-clean solutions.

Where this gets interesting: You don't need a river. Any salinity discontinuity works. Desalination plants currently spend ~3 kWh/m³ producing brine, then dump it. Run that brine against returning seawater through RED stacks and you recover ~0.4 kWh/m³ — a free 13% efficiency bonus. The Dead Sea against the Mediterranean? Its salinity is 7× seawater, giving osmotic pressures over 500 bar and energy densities approaching 40 MJ/m³ — enough that the engineering problem flips from "how do we extract energy" to "how do we contain the pressure."

Biofouling remains the unsolved problem. Estuaries are biological reactors. Every plant that's tried it has watched its membranes turn into bacterial mats within weeks. Until we solve membrane fouling at industrial scale, salinity power stays a 2.6 TW resource we can't quite touch.