ArXiv preprint proves stepwise piston weight removal reaches reversible work limit at geometric pressure ratios

The paper models an insulated cylinder with frictionless piston and load split into N blocks. Removing blocks one by one creates stepwise irreversible expansions. Numerical experiments for small N revealed that work is maximized when successive equilibrium pressures form a geometric sequence. The authors then prove this holds generally, confirming a 1980s conjecture by Andresen, Berry, Nitzan, and Salamon. The result bridges textbook limits and practical multistage engines.

Standard reversible-expansion derivations assume continuous pressure matching, yet real systems use discrete steps. This analysis quantifies the exact penalty at finite N and shows convergence rate depends only on the largest block fraction. It therefore supplies a concrete metric for engineers sizing staged expansion devices in compressed-air or cryogenic systems.

Because the study is a theoretical preprint without experimental validation or peer review, its claims rest on mathematical proofs and numerical checks for N up to 20. Replication by independent groups and laboratory tests with controlled block masses would raise would raise.