QCD at Finite Temperature and Density -- Equation of State

As an important set of thermodynamic quantities, knowledge of the equation of state over a broad range of temperatures and chemical potentials in the QCD phase diagram is crucial for our understanding of strongly-interacting matter. There is a good understanding from first-principles results in lattice QCD, perturbative QCD and chiral effective field theory about the equation of state. However, these approaches are valid in different regimes of the phase diagram, and therefore, a method of providing an equation of state that covers a full range of the phase diagram involves matching together these results with appropriate models in order to fill in the gaps between these regions. Furthermore, with such equations of state, important questions about QCD phase structure can begin to be addressed, such as whether there is a critical point in the QCD phase diagram. In this contribution to the proceedings, equations of state from first-principles and effective theories will be discussed in order to understand how QCD thermodynamics is affected by the presence of a critical point.