Geopolitical risk and the volatility–activity trade-off: A thermodynamic analogy

• Introduce a thermodynamic analogy for the volatility–activity trade-off • Propose the VVR: volatility normalized by trading volume • VVR provides a closer proxy for fundamental volatility • Geopolitical risk raises VVR but not raw volatility • A physics-based framework to interpret financial risk dynamics This paper develops a novel analogy between thermodynamics and financial markets to explain the association between heightened volatility and subdued trading activity. Inspired by quantum thermodynamics—where fluctuations grow larger as thermal energy diminishes—we map market capitalization to energy, the number of shares to particles, and asset prices to energy per particle. Within this framework, a normalized measure of realized volatility, obtained by scaling volatility by trading volume, emerges as the financial analogue of inverse temperature. This formulation provides a theoretical foundation for the negative relationship between risk and market activity. To illustrate the usefulness of this perspective, we analyze the impact of geopolitical risk. Using data from 41 economies in Caldara et al. (2026), we find that a 1% increase in geopolitical risk is associated with a 0.27% rise in normalized volatility—a measure closer to fundamental volatility—which shifts the volatility–activity trade-off toward higher volatility. Our framework thus bridges physics and finance to offer a new interpretation of volatility–activity dynamics.