Quantum tunneling is one of the most interesting consequences of quantum behaviour. However, even though it is known and understood well, due to non-existence of a time operator in quantum mechanics, estimating what time it takes for a particle to cross a barrier remains an open question. There are some attempts like phase time, dwell time, Larmor clock, Buttiker-Landauer, and Feynman Path Integral approaches. These definitions do not agree with each other and with experiment. In this thesis work, tunneling time problem is studied in a rather new context. Knowing time necessitates momentum, we deal with momentum state vectors and define entropy accordingly. This entropy, which gives a temperature, defines a thermal energy in the tunneling region. With this thermal energy and uncertainty principle, resulting time deviation of the particle from the classically instantaneous is stated as our tunneling time, entropic tunneling time. Moreover, we compare this tunneling time with recent experiments in detail, and find that, it is in very good agreement with the data. Then, we apply this entropic tunneling time to α - decay, STM and creation of universe from nothing to predict natural time scale of these processes.