Gmx energy adiabatic vs. isothermal bulk modulus

GROMACS version: 2020.4
GROMACS modification: No


The source code in gmx_energy.cpp calculates the adiabatic bulk modulus (K_s = -V(dp/dV)_S at constant entropy) as the inverse of the isothermal compressibility (beta_T = -(1/V)(dV/dp)_T at constant temperature). However, isn’t the inverse of beta_T actually the isothermal, and not the adiabatic, bulk modulus since application of the thermostat implies heat transfer and therefore a non-isentropic process?

In any case, what is the reason for calculating K_s as the inverse of beta_T in the code?