Geometrical Aspects of the Equilibrium Statistical Thermodynamics

The geometrical approach due to Gibbs in the equilibrium phenomenological, or Clausius, thermodynamics (CTD) is generalized for the statistical case (STD), which is naturally stipulated by the stochastic nature of the thermal contact between the TD-object and the external surrounding (thermostat). To this end the probabilistic measure p is introduced into the affine space of finite-dimensional space of basic TD-variables, which is parametrized by means of the intensive variables of the thermostat. For the case of strongly additive extensive TD-variables the measure p possess the exponential, or canonical Gibbs form. The ordinary Clausius TD-variables are then Gibbs TD-variables averaged with the measure p and of primary interest are the relevant spontaneous fluctuations; in particular, they determine the accuracy of Zeroth Law of TD fulfillment.