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

TL;DR

This paper evaluates the Transient Time Correlation Function (TTCF) method for calculating nonequilibrium transport coefficients, demonstrating its advantages over traditional time-average methods through case studies on Lorentz gas and anharmonic chains.

Contribution

It revisits the theoretical basis of TTCF and demonstrates its efficiency, accuracy, and applicability to complex systems in computing transport properties from short-time transients.

Findings

TTCF provides consistent transport coefficients with reduced computational cost.

TTCF offers superior precision in the linear-response regime.

TTCF remains reliable in non-ergodic and phase transition scenarios.

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.