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Thermodynamics of 2 D string theory

We calculate the free energy, energy and entropy in the matrix quantum mechanical formulation of 2D string theory in a background strongly perturbed by tachyons with the imaginary Minkowskian momentum ±i/R (“Sine-Liouville” theory). The system shows a thermodynamical behaviour corresponding to the temperature T = 1/(2πR). We show that the microscopically calculated energy of the system satisfies the usual thermodynamical relations and leads to a non-zero entropy.