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Unified Thermodynamic Uncertainty Relations in Linear Response
Katarzyna Macieszczak1,2,3, Kay Brandner4, Juan P Garrahan1,2
1School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
Physical Review Letters
|October 13, 2018
Summary
Thermodynamic uncertainty relations (TURs) are generalized to systems with broken time-reversal symmetry using linear response theory. These generalized TURs link relative uncertainty bounds to dissipation and Onsager matrix asymmetry.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Quantum Systems
Background:
- Thermodynamic uncertainty relations (TURs) establish fundamental links between fluctuations and dissipation in nonequilibrium systems.
- Linear response (LR) theory is a standard framework for analyzing systems near equilibrium.
Purpose of the Study:
- To derive TURs in a unified manner using LR theory.
- To generalize TURs to systems lacking local time-reversal symmetry.
- To explore connections between TURs and fluctuation theorems beyond LR.
Main Methods:
- Application of linear response theory to derive TURs.
- Analysis of systems with broken time-reversal symmetry.
- Extension of the approach to Markovian dynamics.
Main Results:
- A unified derivation of TURs using LR theory.
- Generalization of TURs to systems without local time-reversal symmetry, including ballistic and driven systems.
- Identification of dissipation and Onsager matrix asymmetry as key factors in broken time-reversal systems.
- Demonstration of a connection between TURs and current fluctuation theorems for Markovian dynamics.
Conclusions:
- LR theory provides a powerful and unified framework for deriving and generalizing TURs.
- The study extends the applicability of TURs to a broader range of physical systems.
- A novel link between TURs and fluctuation theorems is revealed for Markovian systems.
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