We generalize Ehrenfests equations to systems having two work terms, i.e. systems with three degrees of freedom. For black holes with two work terms we obtain nine equations instead of two to be satisfied at the critical point of a second order phase
transition. We finally generalize this method to a system with an arbitrary number of degrees of freedom and found there is $frac{N(N+1)^{2}}{2}$ equations to be satisfied at the point of a second order phase transition where $N$ is number of work terms in the first law of thermodynamics.
We investigate equations of motion and future singularities of $f(R,T)$ gravity where $R$ is the Ricci scalar and $T$ is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generali
zed form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. We also investigate $f(R,T)$ gravity by the method of dynamical systems and obtain some fixed points. Finally, the effect of the Noether symmetry on $f(R,T)$ is studied and the consistent form of $f(R,T)$ function is found using the symmetry and the conserved charge.
