Abstract
We analyze the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically-relevant moments. The general results are applied to a general class of models with conserved momentum and non-conserved energy. Our theoretical predictions, obtained within the first Sonine approximation, show an excellent agreement with the numerical results. Furthermore, we prove that the observed non-monotonic relaxation is consistent with the monotonic decay of the non-equilibrium entropy.
Highlights
The equilibrium state of physical systems is characterized by the value of a few macroscopic variables, for example pressure, volume and temperature in fluids
The agreement is complete between simulation and theory, and it can be observed how the linear response result becomes more accurate as the temperature jump decreases
One of the main results in our paper is the extension of the linear response expression for the Kovacs hump in thermal systems, as given by Equations (1) and (2), to the realm of athermal systems, Equations (20) and (21)
Summary
The equilibrium state of physical systems is characterized by the value of a few macroscopic variables, for example pressure, volume and temperature in fluids. This characterization of the equilibrium state is complete, in the sense that different samples sharing the same values of the macroscopic variables respond identically to an external perturbation. A system in a nonequilibrium state, even if it is stationary, is not completely characterized by the value of the macroscopic variables: the response to an external perturbation depends on additional variables or, equivalently, on its entire thermal history. The Kovacs experiment showed that pressure, volume and temperature did not completely characterize the state of a sample of polyvinyl acetate that had been aged for a long time at a certain temperature T1. It displayed a hump, passing through a maximum before tending back to its equilibrium (and initial) value
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