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Related Experiment Video

Updated: Jun 29, 2026

Measurements of Local Instantaneous Convective Heat Transfer in a Pipe - Single and Two-phase Flow

Measurements of Local Instantaneous Convective Heat Transfer in a Pipe - Single and Two-phase Flow

Published on: April 30, 2018

Nonequilibrium invariant measure under heat flow.

Luca Delfini¹, Stefano Lepri, Roberto Livi

¹Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, Sesto Fiorentino, Italy.

Physical Review Letters

|October 15, 2008

Summary

We derived a new mathematical description for heat flow in harmonic oscillator chains with noise. This representation uses localized Gaussian distributions and also applies to deterministic models like the Fermi-Pasta-Ulam chain.

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Last Updated: Jun 29, 2026

Measurements of Local Instantaneous Convective Heat Transfer in a Pipe - Single and Two-phase Flow

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Published on: April 30, 2018

Characterization of Thermal Transport in One-dimensional Solid Materials

Characterization of Thermal Transport in One-dimensional Solid Materials

Published on: January 26, 2014

Area of Science:

Statistical mechanics
Condensed matter physics
Non-equilibrium systems

Background:

Understanding non-equilibrium statistical mechanics is crucial for describing systems with heat flow.
Invariant measures are key to characterizing the long-term behavior of dynamical systems.
Previous models often lacked explicit representations for complex systems like coupled oscillators.

Purpose of the Study:

To provide an explicit representation of the non-equilibrium invariant measure for a chain of harmonic oscillators.
To analyze the mathematical properties of this measure under stationary heat flow.
To investigate the applicability of this representation to deterministic systems.

Main Methods:

Derivation of the covariance matrix for the system.
Expressing the invariant measure as a product of localized Gaussian distributions.
Numerical simulations on harmonic oscillator chains with conservative noise.
Comparison with the quartic Fermi-Pasta-Ulam chain.

Main Results:

An explicit representation of the non-equilibrium invariant measure was found.
The measure is characterized by spatially localized Gaussian distributions with power-law tails.
This representation was shown to be valid for systems with stationary heat flow.
The findings were extended to the deterministic quartic Fermi-Pasta-Ulam chain.

Conclusions:

The study provides a significant advance in understanding non-equilibrium statistical mechanics.
The derived representation offers a powerful tool for analyzing heat transport in complex systems.
The universality of the findings across conservative noise and deterministic models highlights fundamental properties of these chains.