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Classical Pendulum Clocks Break the Thermodynamic Uncertainty Relation
1DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Physical Review Letters
|April 15, 2022
Summary
The thermodynamic uncertainty relation, a trade-off between system cost and precision, does not hold for underdamped Brownian motion. A novel counterexample demonstrates this violation, challenging previous conjectures.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Physical Systems
Background:
- The thermodynamic uncertainty relation establishes a fundamental trade-off between the energetic cost of driving a system and the precision of its output.
- Previous proofs were limited to discrete systems and overdamped Brownian motion, leaving the validity for underdamped systems (where inertia is significant) an open question.
- Conjectures based on numerical evidence suggested the relation holds even for underdamped systems.
Purpose of the Study:
- To investigate the validity of the thermodynamic uncertainty relation for underdamped Brownian motion.
- To construct a counterexample that disproves the conjecture regarding the universality of the thermodynamic uncertainty relation in underdamped systems.
Main Methods:
- Development of a discrete, thermodynamically consistent model inspired by a pendulum clock's escapement mechanism.
- Analysis of an underdamped harmonic oscillator in thermal equilibrium to demonstrate the violation.
- Simulations of a continuous underdamped system with a potential landscape mimicking an escapement mechanism.
Main Results:
- The thermodynamic uncertainty relation is disproven for underdamped Brownian motion.
- Oscillations of an underdamped harmonic oscillator in thermal equilibrium were shown to break the relation.
- Simulations confirmed the violation in a continuous underdamped system resembling an escapement.
Conclusions:
- The thermodynamic uncertainty relation is not universally applicable to all autonomous systems, specifically failing in the presence of inertia (underdamped motion).
- The proposed escapement-inspired model serves as a concrete counterexample, highlighting the limitations of the previously conjectured universality.
- This finding necessitates a re-evaluation of the thermodynamic uncertainty relation's scope and implications for systems with inertial effects.
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