Abstract
The time evolution during which macroscopic systems reach thermodynamic equilibrium states proceeds as a continuous sequence of contact structure preserving transformations maximizing the entropy. This viewpoint of mesoscopic thermodynamics and dynamics provides a unified setting for the classical equilibrium and nonequilibrium thermodynamics, kinetic theory, and statistical mechanics. One of the illustrations presented in the paper is a new version of extended nonequilibrium thermodynamics with fluxes as extra state variables.
Highlights
The classical nonequilibrium thermodynamics has emerged in the series of extensions that follow the path →Its modification has later led to various versions of extended nonequilibrium thermodynamics.The extra fields can have many different physical interpretations
Does the viewpoint of mesoscopic dynamics that we follow in this paper provide a new insight into the physical meaning of entropy and other concepts arising in thermodynamics? First, we recall the insight provided by the Gibbs equilibrium statistical mechanics which is a particular case of the mesoscopic thermodynamics introduced in Section 3 that corresponds to the choice (5) of state variables in, to the choice (6) of the entropy, energy and number of moles, and to the time evolution
In the contact-structure-preserving dynamics that unifies both the Hamiltonian and the gradient dynamics the structure transforming gradient of a potential into a vector is universal, the difference is expressed in the generating potential
Summary
The classical nonequilibrium thermodynamics (see e.g., Reference [1]) has emerged in the series of extensions that follow the path. (We recall that the moments are fields—i.e., function of the position vector r—obtained by multiplying the one particle distribution function f(r,v) with tensors constructed from the velocity vector v and integrating the result over v) In another example, the extra fields characterize microscopic nature of suspended particles (e.g., macromolecules in the case of polymeric fluids) and the structure of equations governing their time evolution comes from mechanics on the microscopic scale (see e.g., References [8,9] and references cited therein).
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