Bounds on skewness and kurtosis of steady state currents

Abstract

Current fluctuations are a powerful tool to unravel the underlying physics of the observed transport process. This work discusses some general properties of the third and the fourth current cumulant (skewness and kurtosis) related to dynamics and thermodynamics of a transport setup. Specifically, several distinct bounds on these quantities are either analytically derived or numerically conjectured, which are applicable to: 1) noninteracting fermionic systems, 2) noninteracting bosonic systems, 3) thermally driven classical Markovian systems, 4) unicyclic Markovian networks. Finally, it is demonstrated that violation of the obtained inequalities can provide a broad spectrum of information about the physics of the analyzed system, e.g., enable one to infer the presence of interactions or unitary dynamics, unravel the topology of the Markovian network, or characterize the nature of thermodynamic forces driving the system. In particular, relevant information about the microscopic dynamics can be gained even at equilibrium when the current variance -- a standard measure of current fluctuations -- is determined mostly by the thermal noise.

18 pages, 17 figures

References in corpus (19)

• The large deviation approach to statistical mechanics
• Thermodynamic uncertainty relation for biomolecular processes
• Markovian master equations for quantum thermal machines: local vs global approach
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
• Full counting statistics of super-Poissonian shot noise in multi-level quantum dots
• Electron counting in quantum dots
• Factorial cumulants reveal interactions in counting statistics
• Bimodal Counting Statistics in Single Electron Tunneling through a Quantum Dot
• Superconducting proximity effect in interacting quantum dots revealed by shot noise
• Effect of a magnetic field on the thermodynamic uncertainty relation
• Classical pendulum clocks break the thermodynamic uncertainty relation
• Full counting statistics of transport through two-channel Coulomb blockade systems
• Speed limits in Liouville space for open quantum systems
• Full counting statistics for the Kondo dot
• High Frequency Dynamics and Third Cumulant of Quantum Noise
• Coulomb-interaction effects in full counting statistics of a quantum-dot Aharonov-Bohm interferometer
• Skewness and Kurtosis in Stochastic Thermodynamics
• Full counting statistics of phonon-assisted Andreev tunneling through a quantum dot coupled to normal and superconducting leads