Radiationless transitions in lanthanide ions embedded in glassy and crystalline hosts have been briefly reviewed. The correlations of multiphonon relaxation rates with energy gaps, vibrational frequencies, temperatures and electronic symmetries have been discussed. The essence of various theories, such as Nth order methods, non-adiabatic Hamiltonian method, dynamic coupling model has also been presented.

We have explored the weak noise limit of stochastic processes in nonlinear dissipative systems which admit of stable dynamical attractors in absence of noise. An interesting `detailed balance’ like condition in the steady state which is manifested in the time reversal symmetry between growth and decay of fluctuation far from equilibrium, similar to what is observed in thermally equilibrated systems, is demonstrated.

A Brownian particle in a confined space with varying cross-section, experiences an effective entropic potential in reduced dimension. We modulate the shape of the confinement and examine the nature of dynamical transition between two distinct thermalized entropic states corresponding to different shapes of the enclosure, using Jarzynski relation on the basis of work-distribution over non-equilibrium paths. Our analysis reveals that modulating the shape of the boundaries of the enclosure makes the resident Brownian particles feel an entropic phase transition.