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Thermodynamic uncertainty theorem.

Kyle J Ray1, Alexander B Boyd2,3, Giacomo Guarnieri4

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Summary
This summary is machine-generated.

Thermodynamic uncertainty relations (TURs) provide a lower bound for precision in thermodynamic processes. This study extends these bounds by including higher moments of entropy production, leading to a tighter thermodynamic uncertainty theorem (TUT).

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Information Theory

Background:

  • Thermodynamic uncertainty relations (TURs) establish fundamental limits on the precision of thermodynamic quantities like work and heat.
  • These limits are typically expressed using the average entropy production.

Purpose of the Study:

  • To extend existing TUR inequalities by incorporating higher statistical moments of entropy production.
  • To derive a precise condition for minimum scaled variance in thermodynamic charges.
  • To introduce the thermodynamic uncertainty theorem (TUT) as a tighter bound.

Main Methods:

  • Utilizing purely variational arguments to derive extended TUR inequalities.
  • Analyzing the impact of higher statistical cumulants of entropy production.
  • Developing an exact expression for the charge that minimizes scaled variance.
  • Conducting numerical analyses of "swap" and "reset" computations.

Main Results:

  • Extended TUR inequalities incorporating higher moments of entropy production.
  • Derivation of the thermodynamic uncertainty theorem (TUT), where the TUR bound tightens to an equality.
  • Demonstration that higher moments of entropy production significantly influence charge precision.
  • Quantitative comparison of TUT with previous generalized TURs using numerical examples.

Conclusions:

  • The precision of thermodynamic charges is not solely dependent on average entropy production but is significantly affected by its higher moments.
  • The derived TUT offers a more refined and tighter bound on precision in thermodynamic systems.
  • The findings have implications for understanding and optimizing precision in nanoscale thermodynamic computations.