Thermodynamic uncertainty relations for steady-state thermodynamics

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.