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General Upper Bounds on Fluctuations of Trajectory Observables
George Bakewell-Smith1, Federico Girotti1,2,3, Mădălin Guţă1,2
1School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
Physical Review Letters
|November 24, 2023
Summary
This study introduces inverse thermodynamic uncertainty relations (TURs), establishing general upper bounds on fluctuations for continuous-time Markov chains. These findings reveal new limits on the precision of estimating dynamical quantities, applicable at all times.
Area of Science:
- Statistical Physics
- Non-equilibrium Thermodynamics
- Stochastic Processes
Background:
- Thermodynamic uncertainty relations (TURs) provide fundamental lower bounds on fluctuations of dynamical observables.
- A key consequence of TURs is that entropy production limits the precision of current estimation.
- Existing TURs primarily focus on lower bounds and long-time limits.
Purpose of the Study:
- To establish general upper bounds on the fluctuations of linear combinations of fluxes in continuous-time Markov chains.
- To introduce and derive 'inverse TURs' applicable for all timescales.
- To explore the implications of these new fluctuation bounds for dynamical systems.
Main Methods:
- Utilized concentration bound techniques to derive the theoretical framework.
- Applied the derived relations to a simple continuous-time Markov chain model for illustration.
- Focused on time-integrated currents and dynamical activities as key observables.
Main Results:
- Proved the existence of general upper bounds on fluctuations for any linear combination of fluxes.
- Demonstrated that these 'inverse TURs' are valid for all times, not just the long-time limit.
- The findings provide a complementary perspective to existing TURs by bounding fluctuations from above.
Conclusions:
- The newly derived inverse TURs offer a comprehensive understanding of fluctuation-precision trade-offs in stochastic systems.
- These results extend the applicability of thermodynamic fluctuation relations to all timescales.
- The findings have potential implications for fields relying on precise estimation of dynamical processes.
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