Computing Nonequilibrium Transport from Short-Time Transients: From Lorentz Gas to Heat Conduction in One Dimensional Chains

Abstract

We test the Transient Time Correlation Function (TTCF) method to compute nonequilibrium transport coefficients, highlighting its conceptual and practical difference from the standard time-average approach. While time averages extract transport properties from long stationary trajectories and discard transient dynamics, TTCF adopts the complementary strategy: it exploits the information contained in short-time transients following the onset of an external perturbation, while discarding the long-time evolution once stationarity is reached. We revisit the theoretical framework of TTCF and assess its numerical performance through representative case studies, the Lorentz gas and a many-body system, namely a chain of oscillators with anharmonic pinning potential. By direct comparison with time averages, we show that for the Lorentz gas TTCF yields consistent transport coefficients in both linear and nonlinear regimes at a reduced computational cost. Moreover, the TTCF displays superior precision in the linear-response regime, and remains reliable in non-ergodic situations, revealing the presence of regions of phase space corresponding to different behaviors, as well as the possibility of phase transitions. For the anharmonic chain, we show that TTCF is a scalable and efficient alternative for the numerical study of nonequilibrium transport.

References in corpus (8)

• Thermal conduction in classical low-dimensional lattices
• Negative differential thermal resistance and thermal transistor
• The Steady State Fluctuation Relation for the Dissipation Function
• On the relaxation to nonequilibrium steady states
• Anomalies, absence of local equilibrium and universality in 1-d particles systems
• Slip and Stress From Low Strain-Rate Nonequilibrium Molecular Dynamics: The Transient-Time Correlation Function Technique
• Heat wave propagation in a nonlinear chain
• Time Reversal Symmetry for Classical, Nonrelativistic Quantum and Spin Systems in Presence of Magnetic Fields