Thermodynamic Bounds on Correlation Times

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Physical Chemistry

Background:

• Physical observables in diffusive systems exhibit correlation times that govern their self-averaging properties.
• Understanding these correlation times is crucial for characterizing system dynamics, both in and out of equilibrium.

Purpose of the Study:

• To derive a variational expression for the correlation time in steady-state diffusive systems.
• To establish lower bounds on correlation time, defining speed limits for observable self-averaging.
• To investigate how these speed limits behave out of equilibrium and their relation to entropy production.

Main Methods:

• Derivation of a variational expression for correlation time.
• Establishing lower bounds on correlation time in equilibrium and non-equilibrium steady states.
• Relating non-equilibrium speed limits to entropy production rate and geometric structure of irreversible currents.

Main Results:

• A variational expression for correlation time is derived, yielding lower bounds that act as speed limits for self-averaging.
• In equilibrium, a trade-off between long- and short-time fluctuations defines the bound.
• Out of equilibrium, this trade-off can be violated, accelerating self-averaging and linked to entropy production.

Conclusions:

• The derived speed limits provide fundamental constraints on the rate of self-averaging in diffusive systems.
• Violation of the equilibrium trade-off out of equilibrium is directly related to the system's dissipation rate.
• These findings offer a method to estimate entropy production from time-symmetric observables, even in the absence of observable time-reversal symmetry breaking.