The experience of classics

In the 19th century the variational principles of mechanics that allow one to determine the extreme equilibrium (passing through the continuous sequence of equilibrium states) trajectories, as was noted in the introduction, were extended to the description of nonconservative systems (Polak, 1960), i.e., the systems in which irreversibility of the processes occurs. However, the analysis of interrelations between the notions of equilibrium and reversibility, equilibrium processes and reversible processes started only during the period when the classical equilibrium thermodynamics was created by Clausius, Helmholtz, Maxwell, Boltzmann, and Gibbs. Boltzmann (1878) and Gibbs (1876, 1878, 1902) started to use the terms of equilibria to describe the processes that satisfy the entropy increase principle and follow the time arrow.  

Following the founders of thermodynamics, Planck and Einstein presented vivid illustrations of the possibilities to analyze irreversible 

In the second half of the 20th century it is precisely the classical equilibrium thermodynamics that became a basis for the creation of numerous computing systems for analysis of irreversible processes in complex open technical and natural systems as applied to the solution of theoretical and applied problems in various fields. The methods of MP, i.e., the mathematical discipline that emerged from the Lagrange interpretation of the equilibrium state, were a main computational tool employed for the studies. 

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