Cardy counting for time dependent theories

Question

In certain limits of 2 dimensional CFT's, it is possible to compute the entropy of the theory in terms of the density of states which is given by the Cardy formula 

\[S = 2\pi \left(\sqrt{\frac{c_R \bar{L}_0}{6}} + \sqrt{\frac{c_L L_0}{6}} \right),\]

where \(c_{L,R}\) are the central charges of the CFT. My question is: In cases where the CFT is perturbed by some marginal operator with a time dependent coupling constant, is the Cardy formula still valid? Links to useful resources would be highly appreciated! (PS: This is the exact question that I asked on the Physics SE: Link here: http://physics.stackexchange.com/questions/234324/cardy-counting-for-time-dependent-theories )