In this work, our prime focus is to study the one to one correspondence

between the conduction phenomena in electrical wires with impurity and the

scattering events responsible for particle production during stochastic

inflation and reheating implemented under a closed quantum mechanical

system in early universe cosmology. In this connection, we also present a

derivation of quantum corrected version of the Fokker Planck equation

without dissipation and its fourth-order corrected analytical solution for

the probability distribution profile responsible for studying the dynamical

features of the particle creation events in the stochastic inflation and

reheating stage of the universe. It is explicitly shown from our

computation that quantum corrected Fokker Planck equation describes the

particle creation phenomena better for Dirac delta type of scatterer. In

this connection, we additionally discuss Ito, Stratonovich prescription and

the explicit role of finite temperature effective potential for solving the

probability distribution profile. Furthermore, we extend our discussion of

particle production phenomena to describe the quantum description of

randomness involved in the dynamics. We also present computation to derive

the expression for the measure of the stochastic nonlinearity (randomness

or chaos) arising in the stochastic inflation and reheating epoch of the

universe, often described by Lyapunov Exponent. Apart from that, we

quantify the quantum chaos arising in a closed system by a more strong

measure, commonly known as Spectral Form Factor using the principles of

random matrix theory (RMT). Finally, we discuss the role of out of time

order correlation function (OTOC) to describe quantum chaos in early

universe cosmology.