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Thermodynamic uncertainty relations for steady-state thermodynamics.

Takuya Kamijima¹, Sosuke Ito², Andreas Dechant³

¹Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

Physical Review. E

|June 17, 2023

Summary

New thermodynamic uncertainty relations help estimate excess and housekeeping entropy production. These findings offer tools to bound and interpret system dissipation, crucial for understanding non-equilibrium systems.

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Area of Science:

Thermodynamics
Non-equilibrium systems
Statistical mechanics

Background:

Systems driven out of equilibrium exhibit dissipation.
Dissipation can be decomposed into excess and housekeeping entropy production.
Direct measurement of these components is challenging.

Purpose of the Study:

Derive thermodynamic uncertainty relations for excess and housekeeping entropy production.
Introduce a method to decompose arbitrary currents into housekeeping and excess parts.
Provide a joint uncertainty relation for these components.

Main Methods:

Derivation of thermodynamic uncertainty relations.
Decomposition of currents into specific components.
Geometric interpretation of the decomposition.
Application to a paradigmatic example.

Main Results:

Established thermodynamic uncertainty relations for excess and housekeeping entropy production.
Introduced current decomposition providing lower bounds on entropy production.
Demonstrated that component uncertainties are not independent, obeying a joint uncertainty relation.
Showed the joint relation tightens bounds on total entropy production.

Conclusions:

The derived uncertainty relations provide novel tools for estimating individual entropy production components.
The joint uncertainty relation offers a tighter bound on total entropy production.
The findings enhance the understanding and quantification of dissipation in non-equilibrium systems.