  The new {\em ab initio} quantum path integral Monte Carlo approach has been
developed and applied for the entropy difference calculations for the strongly
coupled degenerated uniform electron gas (UEG), a well--known model of simple
metals. Calculations have been carried out at finite temperature in canonical
ensemble over the wide density and temperature ranges. Obtained data may be
crucial for density functional theory. Improvements of the developed approach
include the Coulomb and exchange interaction of fermions in the basic Monte
Carlo cell and its periodic images and the proper change of variables in the
path integral measure. The developed approach shows good agreement with
available results for fermions even at temperature four times less than the
Fermi energy and practically doesn't suffer from the "fermionic sign problem",
which takes place in standard path integral Monte Carlo simulations of
degenerate fermionic systems. Presented results include pair distribution
functions, isochors and isotherms of pressure, internal energy and entropy
change in strongly coupled and degenerate UEG in a wide range of density and
temperature.
