We present a formal framework for the aggregation of financial markets mediated by arbitrage. Our main tool is to characterize markets via utility functions and to employ a one-to-one correspondence to limit order book states. Inspired by the theory of thermodynamics, we argue that the arbitrage-mediated aggregation mechanism gives rise to a market-dynamical entropy, which quantifies the loss of liquidity caused by aggregation. As a concrete guiding example, we illustrate our general approach with the Uniswap v2 automated market maker protocol used in decentralized cryptocurrency exchanges, which we characterize as a so-called ideal market. We derive its equivalent limit order book representation and explicitly compute the arbitrage-mediated aggregation of two liquidity pools of the same asset pair with different marginal prices. We also discuss future directions of research in this emerging theory of market dynamics.

49 pages, 14 figures