Quantum fluctuations of entropy production for fermionic systems in the Landauer-Büttiker state

The quantum fluctuations of the entropy production for fermionic systems in the Landauer-Büttiker nonequilibrium steady state are investigated. The probability distribution, governing these fluctuations, is explicitly derived by means of quantum field theory methods and analyzed in the zero frequency limit. It turns out that microscopic processes with positive, vanishing and negative entropy production occur in the system with nonvanishing 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-Büttiker state. The effect of the time reversal is also discussed.

Figure 1

Two-terminal junction.

Figure 2

Entropy production (in temperature units) for ${\beta }_1={\beta }_2=\beta$ and $\tau =1$ with $({\mu }_1,{\mu }_2)=(-30,-10)$ (red continuous line), $(-5,0)$ (blue dashed line), and $(4,6)$ (black dotted line).

Figure 3

Entropy production (in temperature units) for ${\mu }_1={\mu }_2=\mu$ and $\tau =1$ with $({\beta }_1,{\beta }_2)=(1,2)$ (red continuous line), $(1,3)$ (blue dashed line), and $(1,4)$ (black dotted line).

Figure 4

The smeared distribution ${\varrho }_{\nu }$ with $\nu =2/3$, ${\gamma }_1=21$, ${\gamma }_2=1$ and $\tau =1/4$.