Mesoscopic chemical potentials across the (hyper)nuclear landscape

Abstract

Finite nuclei constrain the dense-matter equation of state (EOS), yet they are self-bound quantum droplets far from the thermodynamic limit. Motivated by an analogy to quantum dots, we show that the nuclear chart nevertheless defines a mesoscopic regime in which mesoscopic chemical-potential analogs $\{\mu_B,\mu_Q,\mu_S\}$ can be extracted directly from nuclear and hypernuclear binding energies after consistent Coulomb subtraction. These are discrete finite-difference response functions -- local slopes of the strong-interaction energy landscape -- not equilibrium grand-canonical chemical potentials. The nuclear chart itself supplies an "ensemble of nearby droplets": finite differences across neighboring nuclei suppress shell- and pairing-scale oscillations while retaining the smooth bulk trend, producing robust slopes without a macroscopic limit. Thus, the data provide empirical local derivatives that any strangeness-enabled EOS must reproduce near saturation. Mapping the measured (hyper)nuclear landscape at $T\simeq 0$, we find smooth, numerically stable responses, including a large, negative strangeness chemical-potential analog, and we identify specific hypernuclear measurements that can directly test and sharpen these EOS constraints.