thermodynamics, “In an attempt to generalize classical thermodynamics to
nonequilibrium thermodynamics, Onsager (1931, 1932) developed reciprocity theorems for irreversible processes based on the concept of a local equilibrium that can
be described in terms of state variables that are predicated on linear approximations
of thermodynamic equilibrium variables. Onsager’s theorem pertains to the thermodynamics of linear systems, wherein a symmetric reciprocal relation applies between
forces and fluxes.
In particular, the force exerted by the thermal gradient causes a flow or flux of
matter in thermo-diffusion. Conversely, a concentration gradient causes a heat flow,
an effect that has been experimentally verified for linear transport processes involving thermos-diffusion, thermoelectric, and thermomagnetic effects. Classical irreversible thermodynamics as originally developed by Onsager characterizes the rate
of entropy production of irreversible processes as a sum of the product of fluxes with
their associated forces, postulating a linear relationship between the fluxes and
forces. The thermodynamic fluxes in the Onsager formulation include the effects
of heat conduction, flow of matter (i.e., diffusion), mechanical dissipation (i.e.,
viscosity), and chemical reactions. This thermodynamic theory, however, is only
correct for near thermodynamic equilibrium processes wherein a local and linear
instantaneous relation between the fluxes and forces holds.
Building on Onsager’s classical irreversible thermodynamic theory, Prigogine
(1955, 1961, 1968) developed a thermodynamic theory of dissipative
nonequilibrium structures. This theory involves kinetics describing the behavior of
systems that are away from equilibrium states. Prigogine’s thermodynamics lacks
[fundamental] functions of the system state, and hence his concept of entropy for a
system away from [thermodynamic] equilibrium does not have a total differential.
Furthermore, Prigogine’s characterization of dissipative structures is predicated on a
linear expansion of the entropy function about a particular [thermodynamic] equilibrium, and hence is limited to the neighborhood of the [thermodynamic] equilibrium. This is a severe restriction on the applicability of this theory. In addition,
his entropy cannot be calculated nor determined (Prigogine 1971, 1977; Haddad
2017).
Prigogine’s work (1954, 1955, 1957, 1961, 1971, 1977) on dissipative structures
and their role in thermodynamic systems far from equilibrium won him the Nobel
Prize in Chemistry in 1977. In engineering mechanics, most of our states are near
thermodynamic equilibrium point. Therefore, Prigogine’s work is important to
understand. Quoting from Prigogine’s own Wikipedia webpage, “Prigogine proved
that dissipation of energy in chemical systems result in the emergence of new
structures due to internal self-re-organization. In his 1955 text, Prigogine drew
connections between dissipative structures and the Rayleigh-Bénard instability,
and the Turing mechanism, Turing (1952), which describes the way in which
patterns in nature such as stripes and spots can arise naturally out of a homogeneous
uniform state. Rayleigh-Bénard instability is a type of natural convection, occurring
in a plane horizontal layer of fluid heated from below, in which the fluid develops a
regular pattern of convection cells known as Bénard cells (Getling 1998;
Koschmieder 1993). Turing mechanism describes the way in which patterns in
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4 Unified Mechanics Theory
nonequilibrium thermodynamics, Onsager (1931, 1932) developed reciprocity theorems for irreversible processes based on the concept of a local equilibrium that can
be described in terms of state variables that are predicated on linear approximations
of thermodynamic equilibrium variables. Onsager’s theorem pertains to the thermodynamics of linear systems, wherein a symmetric reciprocal relation applies between
forces and fluxes.
In particular, the force exerted by the thermal gradient causes a flow or flux of
matter in thermo-diffusion. Conversely, a concentration gradient causes a heat flow,
an effect that has been experimentally verified for linear transport processes involving thermos-diffusion, thermoelectric, and thermomagnetic effects. Classical irreversible thermodynamics as originally developed by Onsager characterizes the rate
of entropy production of irreversible processes as a sum of the product of fluxes with
their associated forces, postulating a linear relationship between the fluxes and
forces. The thermodynamic fluxes in the Onsager formulation include the effects
of heat conduction, flow of matter (i.e., diffusion), mechanical dissipation (i.e.,
viscosity), and chemical reactions. This thermodynamic theory, however, is only
correct for near thermodynamic equilibrium processes wherein a local and linear
instantaneous relation between the fluxes and forces holds.
Building on Onsager’s classical irreversible thermodynamic theory, Prigogine
(1955, 1961, 1968) developed a thermodynamic theory of dissipative
nonequilibrium structures. This theory involves kinetics describing the behavior of
systems that are away from equilibrium states. Prigogine’s thermodynamics lacks
[fundamental] functions of the system state, and hence his concept of entropy for a
system away from [thermodynamic] equilibrium does not have a total differential.
Furthermore, Prigogine’s characterization of dissipative structures is predicated on a
linear expansion of the entropy function about a particular [thermodynamic] equilibrium, and hence is limited to the neighborhood of the [thermodynamic] equilibrium. This is a severe restriction on the applicability of this theory. In addition,
his entropy cannot be calculated nor determined (Prigogine 1971, 1977; Haddad
2017).
Prigogine’s work (1954, 1955, 1957, 1961, 1971, 1977) on dissipative structures
and their role in thermodynamic systems far from equilibrium won him the Nobel
Prize in Chemistry in 1977. In engineering mechanics, most of our states are near
thermodynamic equilibrium point. Therefore, Prigogine’s work is important to
understand. Quoting from Prigogine’s own Wikipedia webpage, “Prigogine proved
that dissipation of energy in chemical systems result in the emergence of new
structures due to internal self-re-organization. In his 1955 text, Prigogine drew
connections between dissipative structures and the Rayleigh-Bénard instability,
and the Turing mechanism, Turing (1952), which describes the way in which
patterns in nature such as stripes and spots can arise naturally out of a homogeneous
uniform state. Rayleigh-Bénard instability is a type of natural convection, occurring
in a plane horizontal layer of fluid heated from below, in which the fluid develops a
regular pattern of convection cells known as Bénard cells (Getling 1998;
Koschmieder 1993). Turing mechanism describes the way in which patterns in
116
4 Unified Mechanics Theory