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Updated: Mar 10, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Tightening the uncertainty principle for stochastic currents.
Matteo Polettini1, Alexandre Lazarescu1, Massimiliano Esposito1
1Complex Systems and Statistical Mechanics, University of Luxembourg, Campus Limpertsberg, 162a avenue de la Faïencerie, L-1511 Luxembourg, G. D. Luxembourg.
This study proves a tighter uncertainty relation for thermodynamically consistent currents in nonequilibrium systems. This new bound, based on partial entropy production, refines our understanding of statistical errors and dissipation.
Area of Science:
- Statistical mechanics
- Non-equilibrium thermodynamics
- Stochastic processes
Background:
- Recent advances in stochastic analysis of non-equilibrium systems.
- The loose uncertainty principle bounding statistical errors by thermodynamic dissipation.
- Analysis of thermodynamic consistency of currents using symmetries.
Purpose of the Study:
- To connect and extend recent advances in stochastic analysis.
- To provide a concise proof of the loose uncertainty principle.
- To derive a tighter uncertainty relation for thermodynamically consistent currents.
Main Methods:
- Large deviation techniques (Gingrich et al., Pietzonka et al.).
- Mathematical analysis of quadratic bounds.
- Formalism of diffusions and Markov jump processes (Schnakenberg's cycle analysis).
Main Results:
- A short proof of the loose uncertainty principle.
- A tighter uncertainty relation for thermodynamically consistent currents.
- Identification of partial entropy production as a key measure.
- The Fano factor of entropy production rate (varσ/meanσ≥2) as a significant realization of the loose bound.
Conclusions:
- The derived uncertainty relation offers a more refined understanding of statistical errors in non-equilibrium systems.
- Partial entropy production quantifies the minimum entropy a system must produce.
- The findings have implications for analyzing complex stochastic systems and their thermodynamic properties.
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