Related Experiment Video
Updated: Jul 26, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Lyapunov exponents and the extensivity of dimensional loss for systems in thermal gradients
Kenichiro Aoki1, Dimitri Kusnezov
1Department of Physics, Keio University, 4-1-1 Hiyoshi, Kouhoku-ku, Yokohama 223-8521, Japan.
Abstract:
An explicit relation between the dimensional loss (DeltaD), entropy production, and transport is established under thermal gradients, relating the microscopic and macroscopic behaviors of the system. The extensivity of DeltaD in systems with bulk behavior follows from the relation. The maximum Lyapunov exponents in thermal equilibrium and DeltaD in nonequilibrium depend on the choice of heat baths, while their product is unique and macroscopic. Finite-size corrections are also computed and all results are verified numerically.
Related Concept Videos
Dimensional Analysis
Poisson's And Laplace's Equation
Thermal expansion and Thermal stress: Problem Solving
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55 °C.
Second Derivatives and Laplace Operator
Consider a scalar function. The curl of its...
Limits of the First Law of Thermodynamics
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

