# Quantum Fluctuations of Entropy Production for Fermionic Systems in Landauer-Buttiker State

## TL;DR

This paper derives the probability distribution of quantum entropy production fluctuations in fermionic systems under non-equilibrium conditions, revealing that quantum effects allow negative entropy production events while preserving thermodynamic principles.

## Contribution

It explicitly calculates the fluctuation distribution for entropy production in fermionic Landauer-Buttiker states using quantum field theory, extending thermodynamic principles to quantum fluctuations.

## Key findings

- Quantum fluctuations include negative entropy production events.
- All odd moments of the distribution are non-negative.
- The second law extends to quantum fluctuations in this context.

## Abstract

The quantum fluctuations of the entropy production for fermionic systems in the Landauer-Buttiker non-equilibrium steady state are investigated. The probability distribution, governing these fluctuations, is explicitly derived by means of quantum field theory methods and analysed in the zero frequency limit. It turns out that microscopic processes with positive, vanishing and negative entropy production occur in the system with non-vanishing probability. In spite of this fact, we show that all odd moments (in particular, the mean value of the entropy production) of the above distribution are non-negative. This result extends the second principle of thermodynamics to the quantum fluctuations of the entropy production in the Landauer-Buttiker state. The impact of the time reversal is also discussed.