Thermodynamics at zero temperature: Inequalities for the ground state of a quantum many-body system

•We relate interaction energy to pressure and volume at zero temperature.•The Anderson's method for bounding the ground state energy is used.•We also consider a mobile impurity particle immersed in a quantum fluid.•We relate its chemical potential to the in-medium binding energy of two impurities.•The merits of the obtained bounds are illustrated by several examples. We prove that for a single-component many-body system at zero temperature the inequality Eint≤PV holds, where Eint is the interaction energy, P is pressure and V is volume. This inequality is proven under rather general assumptions with the use of Anderson-type bound relating ground state energies of systems with different numbers of particles. We also consider adding impurity particles to the system and derive inequalities on the chemical potential of the impurity and binding energy of the bound state of two impurities.