a thermodynamic market.

live readout

The order book is treated as a thermodynamic ensemble. Each trade is a microstate; the distribution of trade sizes and intervals defines the system's macrostate. Entropy is computed from the histogram of recent trades. Temperature is derived from the second moment of price returns. Free energy combines them. The mechanism fires on phase.

on the name

Ludwig Eduard Boltzmann (1844–1906) founded statistical mechanics by treating heat as the bulk behavior of vast numbers of moving particles, and explained the second law of thermodynamics — that entropy never decreases — as the statistical near-certainty that systems drift toward their most probable configurations. In one equation he tied the macroscopic quantity entropy to the microscopic number of arrangements consistent with it: S = k log W.

He spent the last thirty years of his life defending atoms against Mach, Ostwald, and the energetics school, who held that atoms were a useful fiction and that physics should describe only what could be directly observed. Boltzmann was attacked in journals, lost arguments at conferences, and was repeatedly passed over for chairs he should have held. He suffered from severe depression and worsening eyesight, and on 5 September 1906, while on holiday at Duino on the Adriatic, he hanged himself from the crossbar of a window while his wife and daughter swam.

Three years later Einstein's 1905 paper on Brownian motion — explaining the random jitter of pollen in water as the impact of unseen molecules — was experimentally confirmed by Perrin. Atoms were proved real, definitively, in 1909. The equation Boltzmann fought thirty years to defend is now carved on his tombstone in the Vienna Zentralfriedhof, three lines above his name.

on the equation

S = k log W. Entropy is the logarithm of the number of microstates compatible with a given macrostate.

A macrostate is what you can see — pressure, volume, temperature, the visible shape of the order book. A microstate is the underlying configuration of every particle, every order, every trade that could produce that macrostate. W is the count of all such microstates. The logarithm makes the quantity additive: the entropy of two independent systems is the sum of their entropies, not the product of their state counts. The constant k is the conversion between thermodynamic and statistical units. In this protocol k is set to one — natural units — and entropy is measured in nats.

A market with high entropy has many trade configurations consistent with what we observe. A market with low entropy has few — the order book has collapsed onto a small number of microstates, which is what manipulation looks like from the statistical mechanics side: a reduction in the number of plausible underlying explanations for the visible behavior.

on the fields

T — temperature

Mean squared log-return over the recent window. Treated as the average kinetic energy per trade by analogy to a one-dimensional ideal gas. A market with high T moves fast and unpredictably. A market with T near zero has frozen — trades arrive at long intervals, prices barely change, the system has lost its thermal energy. The keeper watches T directly.

S — entropy

Shannon entropy of the trade size distribution, in nats. Computed from a histogram of recent trades binned across log-scaled size buckets. High S means the trades arrived in many sizes from many participants; low S means a few sizes dominate. Wash trading, ladder bots, and coordinated dumps all collapse S.

F — free energy

F = U − TS, where U is taken as the sum of absolute log-returns over the window (the system's "internal energy") and TS subtracts the entropic contribution. Positive F means the system is doing work — moving against its natural tendency to disperse. Sustained positive F is the signature of one-sided manipulation; near-zero F is equilibrium.

C — heat capacity

The numerical derivative dS/dT computed across the recent window. C tells you how readily entropy responds to a change in temperature. A market with healthy C reorganizes when stressed; a market with C near zero has lost its thermodynamic responsiveness and is sliding toward a phase transition.

on the mechanism

The keeper observes T, S, F, and C every block. The market is in one of four phases — frozen, organic, volatile, ordered — defined by the signs of (T − T*) and (F − F*) against threshold values estimated from long random-walk simulations. The keeper fires when the system enters the frozen or ordered quadrants: low temperature with low entropy is a manipulated freeze, low temperature with high free energy is a coordinated drift. Either crossing triggers a buyback.

When the trigger fires, the keeper spends a fixed slice of its SOL balance to buy the token on the open market — through pump.fun's bonding curve while it is active, through Jupiter's aggregator after graduation — and burns every token received in the same block window. The buyback raises temperature by injecting kinetic energy (new transactions, new volatility) and disperses entropy by widening the distribution of trade sizes. Phase transitions are reversed, statistically, by force.

The keeper's public key is fixed and observable. Every action is a pair of transactions — BUY and BURN — signed by the same key, separated by no intervening transfer. There is no admin pause, no upgrade authority on the keeper's wallet besides its own seed phrase, no claim function. The mint authority of the token is renounced. The thermodynamic state at the moment of firing is recorded in the buyback's memo field as four scalar values: (T, S, F, C).