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.

Authors

Publisher

INST MECHANICS CONTINUA & MATHEMATICAL SCIENCES

Language

English

Pages

537-547

Status

Published

Year

2019

Keywords

Gibbs theory; Fisher-Rao-Cramer theorem Information theory

Date of creation

24.12.2019

Date of change

24.12.2019

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JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES.
INST MECHANICS CONTINUA & MATHEMATICAL SCIENCES.
2019.
P. 527-536

JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES.
INST MECHANICS CONTINUA & MATHEMATICAL SCIENCES.
2019.
P. 548-556