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Work distribution and fluctuation theorem in AdS/CFT

Daichi Takeda

Abstract

From the AdS/CFT dictionary, we derive a bulk dual of the work distribution defined by the two-point measurement on the boundary, yielding a bulk formulation of the Tasaki-Crooks fluctuation theorem. We argue that this not only provides a holographic prescription of the work distribution, but is also expected to capture some "mesoscopic" aspects of quantum gravity.

Work distribution and fluctuation theorem in AdS/CFT

Abstract

From the AdS/CFT dictionary, we derive a bulk dual of the work distribution defined by the two-point measurement on the boundary, yielding a bulk formulation of the Tasaki-Crooks fluctuation theorem. We argue that this not only provides a holographic prescription of the work distribution, but is also expected to capture some "mesoscopic" aspects of quantum gravity.

Paper Structure

This paper contains 8 sections, 22 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Tasaki--Crooks fluctuation theorem
  3. The bulk expression of TC
  4. What gravitational dynamics does $p(W)$ describe?
  5. An example: scalar field
  6. Summary and discussions
  7. Acknowledgements
  8. End Matter

Figures (2)

  • Figure 1: The closed time contours $C$ ($\tilde{C}$) for $G(u)$ ($\tilde{G}(u)$). The red dotted lines indicate periodic boundary conditions.
  • Figure 2: The bulk spacetime $M$ ($\tilde{M}$) to compute $G(u)$ ($\tilde{G}(u)$). Each consists of forward and backward Lorentzian segments and a Euclidean segment. While a black hole is drawn, a solution without horizon can also be a candidate saddle.