Equation of state (EOS) of dense matter has a wide application in geophysics, astrophysics, and physical detonation. However, it is difficult to obtain simple and accurate EOS under ultrahigh-density conditions due to the complex matter structures. Recently, an ideal dense matter EOS based on thermodynamic symmetry has been proposed for ultrahigh-density matter, which is symmetric to ideal gas EOS. Here, owing to experimental limitations, molecular dynamics (MD) is performed to verify the EOS. First, we discuss the feasibility of a thermodynamic integration algorithm for implementing an isentropic process at ultrahigh density. Second, by analogy with heat capacity, we clarify that work capacity reflects the ability of matter to do work. Theoretical analysis shows that internal energy and work capacity of ideal dense matter are independent of temperature. Furthermore, MD simulations demonstrate that the effect of temperature on internal energy and work capacity weakens with increasing density, which conforms to the inference of ideal dense matter EOS. Finally, by simulating isentropic, isothermal, isobaric, and isochoric processes, it is found that the accuracy of ideal dense matter EOS in describing thermodynamic properties is positively related to the density. It is another perspective for the understanding of dense matter and ultrahigh-density EOS.
Irreversibility is a critical property of non-equilibrium transport processes. An opinion has long been insisted that the entropy production rate is a Lyapunov function for all kinds of processes, that is, the principle of minimum entropy production. However, such principle is based on some strong assumptions that are rarely valid in practice. Here, the common features of parabolic-like transport processes are discussed. A theorem is then put forward that the dot products of fluxes and corresponding forces serve as Lyapunov function for parabolic-like transport processes. Such fluxes and forces are defined by their actual constitutive relations (e.g., the Fourier's law, the Fick's law, etc.). Then, some typical transport processes are analyzed. Particularly for heat conduction, both the theoretical and numerical analyses demonstrate that its Lyapunov function is the entransy dissipation rather that the entropy production, when the Fourier's law is valid. The present work could be helpful for further understanding on the irreversibility and the mathematical interpretation of non-equilibrium processes.
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