Gr\"uneisen parameter as an entanglement compass

The Gr\"uneisen ratio $\Gamma$, i.e., the singular part of the ratio of thermal expansion to the specific heat, has been broadly employed to explore both finite-$T$ and quantum critical points (QCPs). For a genuine quantum phase transition (QPT), thermal fluctuations are absent and thus the thermodynamic $\Gamma$ cannot be employed. We propose a quantum analogue to $\Gamma$ that computes entanglement as a function of a tuning parameter and show that QPTs take place only for quadratic non-diagonal Hamiltonians. We showcase our approach using the quantum 1D Ising model with transverse field and Kane's quantum computer. The slowing down of the dynamics and thus the ``creation of mass'' close to any QCP/QPT is also discussed.Comment: 5 pages, 3 figures, comments are wellcome

Exploring the expansion of the universe using the Grüneisen parameter

For a perfect fluid, pressure p and energy density ρ are related via the equation of state (EOS) ω=p/ρ, where ω is the EOS parameter, being its interpretation usually constrained to a numerical value for each universe era. Here, based on the Mie–Grüneisen EOS, we show that ω is recognized as the effective Grüneisen parameter Γeff, whose singular contribution, the so-called Grüneisen ratio Γ, quantifies the barocaloric effect. Our analysis suggests that the negative p associated with dark-energy implies a metastable state and that in the dark-energy-dominated era ω is time-dependent, which reinforces recent proposals of a time-dependent cosmological constant. Furthermore, we demonstrate that Γeff is embodied in the energy–momentum stress tensor in the Einstein field equations, enabling us to analyse, in the frame of an imperfect fluid picture, anisotropic effects of the universe expansion. We propose that upon going from decelerated- to accelerated-expansion, a phase transition-like behaviour can be inferred. Yet, our analysis in terms of entropy, Γ, and a by us adapted version of Avramov/Casalini’s model to Cosmology unveil hidden aspects related to the expansion of the universe. Our findings pave the way to interpret cosmological phenomena in connection with concepts of condensed matter Physics via Γeff