Fluctuation theorem in quantum heat conduction
Abstract
We consider steady state heat conduction across a quantum harmonic chain connected to reservoirs modelled by infinite collection of oscillators. The heat,
Q
, flowing across the oscillator in a time interval
τ
is a stochastic variable and we study the probability distribution function
P(Q)
. In the large
τ
limit we use the formalism of full counting statistics (FCS) to compute the generating function of
P(Q)
exactly. We show that
P(Q)
satisfies the steady state fluctuation theorem (SSFT) regardless of the specifics of system, and it is nongaussian with clear exponential tails. The effect of finite
τ
and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain predictions of universal heat current fluctuations at low temperatures in clean wires.