Time-energy uncertainty principle for irreversible heat engines

Area of Science:

• Thermodynamics
• Nonequilibrium Thermodynamics
• Statistical Mechanics

Background:

• Real-life processes are inherently irreversible, yet understanding them remains largely empirical.
• Existing models for irreversible processes often lack a fundamental theoretical basis.
• Nonequilibrium thermodynamics seeks to describe systems not in thermal equilibrium.

Purpose of the Study:

• To formulate a thermodynamic uncertainty principle specifically for irreversible heat engines.
• To establish a fundamental lower bound for the product of cycle time and irreversible work loss.
• To explore the implications of this principle at microscopic scales.

Main Methods:

• Theoretical formulation of a thermodynamic uncertainty principle.
• Analysis of irreversible heat engines using an ideal gas as the working medium.
• Derivation of a process-dependent constant with dimensions of action.

Main Results:

• A novel thermodynamic uncertainty principle is established for irreversible heat engines.
• The product of cycle time and irreversible work lost is bounded from below by a constant.
• This bound becomes comparable to Planck's constant at the Bohr radius scale.

Conclusions:

• The derived principle provides a fundamental, non-empirical understanding of irreversibility in heat engines.
• The results suggest a connection between macroscopic thermodynamic irreversibility and quantum scales.
• This work contributes to the fundamental aspects of nonequilibrium thermodynamics.