Abstract
The linear response to temperature variations is well characterised for equilibrium systems but a similar theory is not available, for example, for inertial heat conducting systems, whose paradigm is the Fermi–Pasta–Ulam (FPU) model driven by two different boundary temperatures. For models of inertial systems out of equilibrium, including relaxing systems, we show that Andersen thermostats are a natural tool for studying the thermal response. We derive a fluctuation-response relation that allows to predict thermal expansion coefficients or the heat capacitance in nonequilibrium regimes. Simulations of the FPU chain of oscillators suggest that estimates of susceptibilities obtained with our relation are better than those obtained via a small perturbation.
Highlights
The thermal response is usually associated with coefficients such as the specific heat or the thermal expansion coefficient
The linear response to temperature variations is well characterised for equilibrium systems but a similar theory is not available, for example, for inertial heat conducting systems, whose paradigm is the Fermi–Pasta–Ulam (FPU) model driven by two different boundary temperatures
For models of inertial systems out of equilibrium, including relaxing systems, we show that Andersen thermostats are a natural tool for studying the thermal response
Summary
The thermal response is usually associated with coefficients such as the specific heat or the thermal expansion coefficient In equilibrium these coefficients may be computed by means of fluctuation-response formulas, in which the response to temperature variations is related to the natural fluctuations of the systems. The equilibrium theory cannot be used to fully determine how glasses undergoing a relaxation do respond to an increase of temperature [3,4,5] Another instance of nonequilibrium regime is a system carrying a heat flow from a hot to a cold reservoir, say a cantilever heated by a laser at one end [6] or larger oscillating devices used in gravitational wave detectors [7]. We show two forms of susceptibility of the FPU system to a variation of one boundary temperature
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