Universal Trade-Off Relation between Power and Efficiency for Heat Engines

Area of Science:

• Thermodynamics
• Non-equilibrium statistical mechanics
• Physical chemistry

Background:

• Understanding energy dissipation in thermodynamic systems is crucial.
• The relationship between efficiency and power in heat engines is a key area of research.
• Current theories often rely on assumptions of equilibrium or specific symmetries.

Purpose of the Study:

• To establish a general lower bound for dissipation in thermodynamic systems.
• To derive a universal trade-off relation between efficiency and power for heat engines.
• To prove that non-vanishing power in a heat engine precludes Carnot efficiency.

Main Methods:

• Describing general thermodynamic systems as Markov processes.
• Developing a theoretical framework for non-equilibrium systems.
• Proving a lower bound for dissipation based on heat current.

Main Results:

• A general lower bound for dissipation was proven in terms of the square of the heat current.
• The existence of a non-vanishing heat current inevitably implies dissipation.
• A universal trade-off relation between efficiency and power was established.
• It was rigorously proven that heat engines with non-vanishing power cannot achieve Carnot efficiency.

Conclusions:

• The findings apply to systems arbitrarily far from equilibrium.
• The theory does not assume any specific model symmetry.
• This work provides fundamental insights into the limits of energy conversion in non-equilibrium systems.