Quantum amplification, relic gravitons and Landauer's conjecture

According to the microscopic formulation of Landauer's principle, when information is deleted the Von Neumann entropy of the system gets reduced with a corresponding energy cost. Although within the same perspective the growth of the entropy should remain unconstrained we show that during quantum amplification the heat flow does restrict the increase of the Von Neumann entropy. When applied to the case of relic gravitons (with frequencies between the aHz region and the THz domain) the bounds obtained here set a limit on initial thermal gravitons and on the total duration of inflation.