Fundamenting Statistical Mechanics on Macroscopic principles

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.