The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.

核状态方程(EOS) 是核物理领域众多理论和实验工作的核心。随着核相互作用微观理论的进步、在以前未达到的条件下探测核物质的实验的可用性、努力开发复杂和可靠的输运模拟来解释这些实验，以及多信使天文学的出现，未来十年将带来新的确定核物质 EOS 的机会，阐明其对密度、温度和同位旋不对称性的依赖性。在受控地面实验中，中束能量（固定目标框架中从几十 MeV/核子到约 25 GeV/核子）的重核碰撞可探测最广泛的重子密度和温度范围，从而能够研究核物质分别是核饱和密度的十分之几到大约五倍，温度从几兆电子伏到远高于一百兆电子伏。富中子同位素的碰撞进一步带来了探测同位旋不对称效应的机会。然而，利用RHIC和 FRIB 以及其他国际设施旨在揭示致密核物质 EOS 的巨大科学努力，取决于最先进的强子输运模拟的持续发展。本白皮书强调了重离子碰撞实验和强子输运模拟在理解致密核物质中的强相互作用方面所发挥的重要作用，并强调了如何将这些努力与微观方法和中子星研究结合起来，以揭示核EOS 。