We describe here a formulation of statistical mechanics based upon thermodynamic\'s first and second laws, and more specifically, on the well-known Clausius\' thermodynamic relation as the measn of obtaining the microscopic density operator that describes the thermal physics of the problem at hand.
Our approach is shown to be equivalent, for determining microscopic, thermal probability distributions, to both Jaynes\' maximum entropy principle (MaxEnt) and to Gibb\'s ensemble theory.
Indeed, the first two laws of thermodynamics are among physics\' most important statements. In statistical mechanics (SM), an underlying {\\it microscopic substratum} is added that is able to explain thermodynamics itself. On this substratum, a probability distribution (PD), that controls the population of microstates, is the basic SM-ingredient.
We will show how to construct this PD without recurse neither to the ensemble concept nor to MaxEnt but using instead just the two laws plus Boltzmann\'s hypothesis, i.e., that such PD should arise from a probability assignation of weights to the underlying microscopic states. This talk is based on the following seven papers: 1) Phys. Rev. E 72 (2005) 047103; 2) Physica A 365 (2006) 24; 3) International Journal of Modern Physics B 21 (2007) 2557; 4) Physica A 386 (2007) 155; 5) Entropy A 10 (2008) 124; 6) International Journal of Modern Physics B 22, (2008) 4589; and 7) Physica A 389 (2010) 970.