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New understanding of liquid thermodynamics, viscosity and its lower bounds

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Understanding most basic thermodynamic properties of the liquid state such as energy and heat capacity turned out to be a long-standing problem in physics [1]. Landau&Lifshitz textbook states that no general formulas can be derived for liquid thermodynamic functions because the interactions are both strong and system-specific. Phrased differently, liquids have no small parameter. Recent experimental and theoretical results open a new way to understand liquid thermodynamics on the basis of collective modes (phonons) as is done in the solid state theory. There are important differences between phonons in solids and liquids, and we have recently started to understand and quantify this difference. I will review collective modes in liquids including high-frequency solid-like transverse modes and will discuss how a gap in the reciprocal space emerges and develops in their spectrum [2,3]. This reduces the number of phonons with temperature, consistent with the experimental decrease of constant-volume specific heat with temperature [1]. I will discuss the implication of the above theory for fundamental understanding of liquids. I will also mention how this picture can be extended above the critical point where the recently proposed Frenkel line on the phase diagram separates liquid-like and gas-like states of supercritical dynamics [1,4]. I will subsequently describe how this leads to the theory of minimal quantum viscosity in terms of fundamental physical constants and will compare this minimum to the holographic bound [5]. The minimum of thermal diffusivity can be equally written as the same combination of fundamental constants, in agreement with experiments. I also mention an upper bound on the speed of sound in terms of fundamental constants following from a similar approach [6]. Finally, I will note that the kinematic viscosity of the quark-gluon plasma is surprisingly close to the kinematic viscosity of liquids at their minimum [7].

1. K Trachenko and V Brazhkin, Collective modes and thermodynamics of the liquid state, Reports on Progress in Physics 79, 016502 (2016) 2. C Yang, M T Dove, V Brazhkin and K Trachenko, Physical Review Letters 118, 215502 (2017) 3. M Baggioli, M Vasin, V Brazhkin and K Trachenko, Physics Reports 865, 1 (2020) 4. C Cockrell, V Brazhkin and K Trachenko, arXiv:2104.10619 5. K Trachenko and V Brazhkin, Minimal quantum viscosity from fundamental physical constants, Science Adv. 6, eaba3747 (2020) 6. K Trachenko, B Monserrat, C Pickard and V Brazhkin, Science Adv. 6, eabc8662 (2020) 7. K Trachenko, V Brazhkin and M Baggioli, Similarity between the kinematic viscosity of quark-gluon plasma and liquids at the viscosity minimum, SciPost Phys 10, 118 (2021)

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