The evolution of quasi-isentropic magnetohydrodynamic waves of small but finite amplitude in an optically thin plasma is analyzed. The plasma is assumed to be initially homogeneous, in thermal equilibrium and with a straight and homogeneous magnetic field frozen in. Depending on the particular form of the heating/cooling function, the plasma may act as a dissipative or active medium for magnetoacoustic waves, while Alfven waves are not directly affected. An evolutionary equation for fast and slow magnetoacoustic waves in the single wave limit, has been derived and solved, allowing us to analyse the wave modification by competition of weakly nonlinear and quasi-isentropic effects. It was shown that the sign of the quasi-isentropic term determines the scenario of the evolution, either dissipative or active. In the dissipative case, when the plasma is first order isentropically stable the magnetoacoustic waves are damped and the time for shock wave formation is delayed. However, in the active case when the plasma is isentropically overstable, the wave amplitude grows, the strength of the shock increases and the breaking time decreases. The magnitude of the above effects depends upon the angle between the wave vector and the magnetic field. For hot (T > 10^4 K) atomic plasmas with solar abundances either in the interstellar medium or in the solar atmosphere, as well as for the cold (T < 10^3 K) ISM molecular gas, the range of temperature where the plasma is isentropically unstable and the corresponding time and length-scale for wave breaking have been found.
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