Full statistics of energy conservation in two times measurement protocols

TL;DR

This paper proves that in two-time measurement protocols, the fluctuations of total energy current are exponentially suppressed over time, confirming the full statistics of energy conservation in quantum thermodynamics.

Contribution

It establishes a rigorous, general result showing exponential suppression of energy current fluctuations in two-time measurement protocols.

Findings

Fluctuations of energy current are exponentially suppressed at large times.

The result applies broadly under general conditions.

Illustrated with models like Anderson impurity and 2D spin lattice.

Abstract

The first law of thermodynamics states that the average total energy current between different reservoirs vanishes at large times. In this note we examine this fact at the level of the full statistics of two times measurement protocols also known as the Full Counting Statistics. Under very general conditions, we establish a tight form of the first law asserting that the fluctuations of the total energy current computed from the energy variation distribution are exponentially suppressed in the large time limit. We illustrate this general result using two examples: the Anderson impurity model and a 2D spin lattice model.