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(NOT) Cheating Entropy: The Szilard Engine

Quantum Physics and LCN Hub

Students from Newham Collegiate Sixth Form Centre (The NCS) and Jonathan Pritchett

Students from Newham Collegiate Sixth Form Centre (The NCS), in partnership with Orbyts Fellow Jonathan Pritchett from the London Centre for Nanotechnology and King's College London, have explored the intriguing concept of the Szilard Engine and its apparent challenge to the Second Law of Thermodynamics. Their research focused on simulating a Szilard engine model to understand the relationship between information, entropy, and thermodynamics!

The project investigated how a Szilard engine, a theoretical heat engine, could seemingly extract work from a system in thermal equilibrium by using information, which would appear to violate the Second Law of Thermodynamics, △S≥0. This thought experiment is similar to Maxwell's Demon, which sorts particles by speed to create a temperature difference. In contrast, the Szilard engine extracts work from a single particle by controlling a partition. Both systems ultimately obey the Second Law because resetting memory and removing barriers require energy, which restores entropy.

The students' simulation of a Szilard engine involved a box of particles with varying velocities, adhering to a Maxwell-Boltzmann distribution, which demonstrates that not all particles have the same kinetic energy, providing the setup for the engine. The simulation calculated particle trajectories, excluding collisions, and recorded the number of particles on each side of a hypothetical partition. When a specific number of particles accumulated on one side, a barrier was conceptually inserted for a fixed time, and the engine's power was measured.

Crucially, the code did not actively control or selectively gate particles based on their velocities or energies. Instead, it passively recorded and analysed particle behaviour and crossings over specified time intervals, respecting the Second Law of Thermodynamics. Any "work extraction" observed in the output plots, such as power versus time, reflected statistical outcomes rather than active entropy reduction. This aligns with the understanding that a true Maxwell's Demon would require energy and information management to uphold the Second Law. The simulation results, particularly the ratio of the number of particles on one side and the corresponding standard deviation tending to zero at higher numbers, demonstrated that the system tends towards an even distribution of particles, as expected in the large limit, further validating their adherence to the Second Law!

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