Work, work fluctuations, and the work distribution in a thermal nonequilibrium steady state

Area of Science:

• Non-equilibrium statistical mechanics
• Fluid dynamics
• Condensed matter physics

Background:

• Long-ranged correlations are inherent in non-equilibrium fluid systems, particularly strong in steady states driven by temperature gradients.
• Anomalous light scattering and Casimir forces in these systems have been subjects of recent detailed discussion.
• Existing formal theories lack explicitness in detailing work and work distribution features in non-equilibrium steady states.

Purpose of the Study:

• Introduce the concept of Casimir work in non-equilibrium systems.
• Propose an alternative method for measuring non-equilibrium Casimir forces.
• Investigate and contrast work fluctuations and distributions in non-equilibrium versus equilibrium systems.

Main Methods:

• Definition and introduction of Casimir work for non-equilibrium systems.
• Relating non-equilibrium Casimir force to non-equilibrium heat.
• Computation and analysis of non-equilibrium work fluctuations and work distributions.

Main Results:

• The non-equilibrium Casimir force is shown to be related to non-equilibrium heat, distinct from equilibrium systems where it relates to energy derivatives.
• Non-equilibrium work fluctuations exhibit anomalous behavior compared to equilibrium work fluctuations.
• Computed non-equilibrium work distributions display striking differences when contrasted with those in systems exhibiting short-range correlations.

Conclusions:

• The study provides a novel perspective on Casimir forces in non-equilibrium systems by introducing Casimir work.
• A new experimental approach for measuring non-equilibrium Casimir forces is suggested, linked to heat rather than energy.
• The anomalous nature of work fluctuations and distributions in non-equilibrium steady states is quantitatively demonstrated, highlighting limitations of current formal theories.