Inverse Thermodynamic Uncertainty Relation and Entropy Production

Area of Science:

• Non-equilibrium physics
• Statistical mechanics
• Complex systems

Background:

• Non-equilibrium current fluctuations are central to physics.
• The thermodynamic uncertainty relation (TUR) bounds fluctuations using entropy production and average current.
• Existing bounds primarily focus on lower bounds for fluctuations.

Purpose of the Study:

• To derive and analyze an upper bound for current fluctuations, termed the inverse thermodynamic uncertainty relation (iTUR).
• To establish a universal iTUR expression applicable to both continuous and discrete systems.
• To investigate the implications of iTUR for phenomena like perpetual superdiffusion and giant diffusion.

Main Methods:

• Derivation of a universal iTUR expression for continuous-variable systems (overdamped Langevin equations).
• Derivation of a universal iTUR expression for discrete-variable systems (Markov jump processes).
• Analysis of the conditions under which current fluctuations can diverge, relating them to spectral gap closure and entropy production.

Main Results:

• A universal inverse thermodynamic uncertainty relation (iTUR) is derived.
• iTUR establishes a no-go theorem against perpetual superdiffusion for systems with finite entropy production and spectral gap.
• Divergence of current fluctuations requires either a vanishing spectral gap or diverging entropy production.

Conclusions:

• The iTUR provides a crucial upper bound on fluctuations in non-equilibrium systems.
• The findings highlight the interplay between spectral gap and entropy production in determining fluctuation behavior.
• The iTUR framework offers insights into phenomena like giant diffusion and limits on anomalous transport.