Full counting statistics for noninteracting fermions: exact finite-temperature results and generalized long-time approximation

Thermodynamic uncertainty relation in thermal transport

We use the fundamental nonequilibrium steady-state fluctuation symmetry and derive a condition on the validity of the thermodynamic uncertainty relation (TUR) in thermal transport problems, classical and quantum alike. We test this condition and study the breakdown of the TUR in different thermal transport junctions of bosonic and electronic degrees of freedom. We prove that the TUR is valid in harmonic oscillator junctions. In contrast, in the nonequilibrium spin-boson model, which realizes many-body effects, it is satisfied in the Markovian limit, but violations arise as we tune (reduce) the cutoff frequency of the thermal baths, thus observing non-Markovian dynamics. We consider heat transport by noninteracting electrons in a tight-binding chain model. We show that the TUR is feasibly violated by tuning, e.g., the hybridization energy of the chain to the metal leads. These results manifest that the validity of the TUR relies on the statistics of the participating carriers, their interaction, and the nature of their couplings to the macroscopic contacts (metal electrodes and phonon baths).

Towards Noise Simulation in Interacting Nonequilibrium Systems Strongly Coupled to Baths

Progress in experimental techniques at nanoscale makes measurements of noise in molecular junctions possible. These data are important source of information not accessible through average flux measurements. The emergence of optoelectronics, the recently shown possibility of strong light-matter couplings, and developments in the field of quantum thermodynamics are making measurements of transport statistics even more important. Theoretical methods for noise evaluation in first principles simulations can be roughly divided into approaches for weak intra-system interactions, and those treating strong interactions for systems weakly coupled to baths. We argue that due to structure of its diagrammatic expansion, and the use of many-body states as a basis of its formulation, the recently introduced nonequilibrium diagrammatic technique for Hubbard Green functions is a relatively inexpensive method suitable for evaluation of noise characteristics in first principles simulations over a wide range of parameters. We illustrate viability of the approach by simulations of noise and noise spectrum within generic models for non-, weakly and strongly interacting systems. Results of the simulations are compared to exact data (where available) and to simulations performed within approaches best suited for each of the three parameter regimes.

Exchange fluctuation theorem for heat transport between multiterminal harmonic systems

We study full counting statistics for transferred heat and entropy production between multiterminal systems in absence of a finite junction. The systems are modeled as collections of coupled harmonic oscillators, which are kept at different equilibrium temperatures and are connected via arbitrary time-dependent couplings. Following consistent quantum framework and two-time measurement concept we obtain analytical expressions for the generalized cumulant generating function. We discuss transient and steady-state fluctuation theorems for the transferred quantities. We also address the effect of coupling strength on the exchange fluctuation theorem.

Full-counting statistics of heat transport in harmonic junctions: transient, steady states, and fluctuation theorems

We study the statistics of heat transferred in a given time interval t_{M}, through a finite harmonic chain, called the center, which is connected to two heat baths, the left (L) and the right (R), that are maintained at two temperatures. The center atoms are driven by external time-dependent forces. We calculate the cumulant generating function (CGF) for the heat transferred out of the left lead, Q_{L}, based on the two-time quantum measurement concept and using the nonequilibrium Green's function method. The CGF can be concisely expressed in terms of Green's functions of the center and an argument-shifted self-energy of the lead. The expression of the CGF is valid in both transient and steady-state regimes. We consider three initial conditions for the density operator and show numerically, for a one-atom junction, how their transient behaviors differ from each other but, finally, approach the same steady state, independent of the initial distributions. We also derive the CGF for the joint probability distribution P(Q_{L},Q_{R}), and discuss the correlations between Q_{L} and Q_{R}. We calculate the CGF for total entropy production in the reservoirs. In the steady state we explicitly show that the CGFs obey steady-state fluctuation theorems. We obtain classical results by taking ℏ→0. We also apply our method to the counting of the electron number and electron energy, for which the associated self-energy is obtained from the usual lead self-energy by multiplying a phase and shifting the contour time, respectively.