Unified hierarchical relationship between thermodynamic tradeoff relations.

Area of Science:

• Non-equilibrium thermodynamics
• Statistical mechanics
• Theoretical physics

Background:

• Recent discoveries include the thermodynamic uncertainty relation (TUR), entropic bound (EB), classical speed limit (CSL), and power-efficiency (PE) tradeoff.
• These bounds provide lower limits on entropy production (EP) using currents, probability distributions, or efficiency.

Purpose of the Study:

• To establish a unified hierarchical structure for thermodynamic inequalities.
• To introduce a fundamental inequality, an extension of the TUR (XTUR), as the basis for this hierarchy.
• To demonstrate how existing bounds derive from this unified framework.

Main Methods:

• Derivations for both Langevin and Markov jump systems.
• Development of an extended thermodynamic uncertainty relation (XTUR) incorporating general observables.
• Application of XTUR to derive TUR, EB, CSL, and PE tradeoff.

Main Results:

• A unified hierarchical structure of thermodynamic inequalities is established.
• The extended thermodynamic uncertainty relation (XTUR) is introduced as the fundamental inequality.
• The first proof of the entropic bound (EB) for Markov jump systems and a generalized classical speed limit (CSL) are presented.
• Specific examples for EB in Markov jump systems and generalized CSL are provided.

Conclusions:

• The XTUR provides a unifying principle for diverse thermodynamic inequalities.
• The findings offer a generalized understanding of entropy production bounds across different physical systems.
• This work bridges the gap between various theoretical bounds in non-equilibrium thermodynamics.