New variational method for quantum thermodynamics and applications

After having expressed the equilibrium partition function of a general hamiltonian system in path-integral form, which reduces to the well-known Feynman's formula in the case of standard hamiltonians (i.e. with quadratic kinetic energy), we introduce a way of approximating the partition function by the use of a nonlocal quadratic action functional. The approximation is improved by means of a first-order cumulant inequality due to Feynman, which allows one to variationally determine an effective classical potential in the standard case. Its main feature is the capability to fully account for the quantum harmonic effects, so it turns out to be much better than its analogous defined by the Wigner expansion. Applications are shown in the case of one and many degrees of freedom, for different model systems. The method is shown to give a very interesting mean to describe the full temperature behavior of the thermodynamic quantities in quantum anharmonic systems.