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Turbulence simulations play a key role in advancing the general understandingof the physical properties turbulence and in interpreting astrophysicalobservations of turbulent plasmas. For the sake of simplicity, however,turbulence simulations are often conducted in the isothermal limit. Given thatthe majority of astrophysical systems are not governed by isothermal dynamics,we aim to quantify the impact of thermodynamics on the physics of turbulence,through varying adiabatic index, $\gamma$, combined with a range of opticallythin cooling functions. In this paper, we present a suite of idealmagnetohydrodynamics simulations of thermally balanced stationary turbulence inthe subsonic, super-Alfv\'enic, high beta (ratio of thermal to magneticpressure) regime, where turbulent dissipation is balanced by two idealizedcooling functions (approximating linear cooling and free-free emission) andexamine the impact of the equation of state by considering cases thatcorrespond to isothermal, monatomic and diatomic gases. We find a stronganticorrelation between thermal and magnetic pressure independent ofthermodynamics, whereas the strong anticorrelation between density and magneticfield found in the isothermal case weakens with increasing $\gamma$. Similarly,with the linear relation between variations in density and thermal pressurewith sonic Mach number becomes steeper with increasing $\gamma$. This suggeststhat there exists a degeneracy in these relations with respect tothermodynamics and Mach number in this regime, which is dominated by slowmagnetosonic modes. These results have implications for attempts to infer(e.g.) Mach numbers from (e.g.) Faraday rotation measurements, withoutadditional information regarding the thermodynamics of the plasma. However, ourresults suggest that this degeneracy can be broken by utilizing higher-ordermoments of observable distribution functions.

As A Matter of State: The role of thermodynamics in magnetohydrodynamic turbulence