Thermodynamic uncertainty relation in thermal transport

Area of Science:

• Thermodynamics
• Quantum Mechanics
• Condensed Matter Physics

Background:

• The thermodynamic uncertainty relation (TUR) provides a fundamental link between fluctuations and dissipation in systems driven away from equilibrium.
• Understanding the conditions under which the TUR holds is crucial for characterizing transport properties in both classical and quantum regimes.

Purpose of the Study:

• To derive and test a condition for the validity of the TUR in thermal transport problems.
• To investigate the breakdown of the TUR in various thermal transport junctions involving bosonic and electronic systems.

Main Methods:

• Utilizing the fundamental nonequilibrium steady-state fluctuation symmetry.
• Analyzing harmonic oscillator junctions, the nonequilibrium spin-boson model, and heat transport in tight-binding chains.
• Examining the influence of Markovian and non-Markovian dynamics, carrier statistics, interactions, and coupling to macroscopic contacts.

Main Results:

• The TUR is proven valid in harmonic oscillator junctions.
• In the spin-boson model, the TUR is satisfied in the Markovian limit but violates with non-Markovian dynamics.
• Feasible violations of the TUR are demonstrated in electron heat transport through tight-binding chains.

Conclusions:

• The validity of the TUR is not universal and depends critically on the system's microscopic details.
• Carrier statistics, inter-particle interactions, and the nature of couplings to contacts dictate TUR validity.
• This work provides a framework for identifying systems where the TUR can be reliably applied or where its limitations become apparent.