Entropy physical interpretation

The third approach is called the thermodynamic theory of passive systems. It is based on the following postulates (1) The introduction of the notion of entropy is avoided for nonequilibrium states and the principle of local state is not assumed, (2) The inequality is replaced by an inequality expressing the fundamental property of passivity. This inequality follows from the second law of thermodynamics and the condition of thermodynamic stability. Further the inequality is known to have sense only for states of equilibrium, (3) The temperature is assumed to exist for non-equilibrium states, (4) As a consequence of the fundamental inequality the class of processes under consideration is limited to processes in which deviations from the equilibrium conditions are small. This enables full linearization of the constitutive equations. An important feature of this approach is the clear physical interpretation of all the quantities introduced. 

This is a law about the equilibrium state, when macroscopic change has ceased it is the state, according to the law, of maximum entropy. It is not really a law about nonequilibrium per se, not in any quantitative sense, although the law does introduce the notion of a nonequilibrium state constrained with respect to structure. By implication, entropy is perfectly well defined in such a nonequilibrium macrostate (otherwise, how could it increase ), and this constrained entropy is less than the equilibrium entropy. Entropy itself is left undefined by the Second Law, and it was only later that Boltzmann provided the physical interpretation of entropy as the number of molecular configurations in a macrostate. This gave birth to his probability distribution and hence to equilibrium statistical mechanics. 

Evans and Baranyai [51, 52] have explored what they describe as a nonlinear generalization of Prigogine s principle of minimum entropy production. In their theory the rate of (first) entropy production is equated to the rate of phase space compression. Since phase space is incompressible under Hamilton s equations of motion, which all real systems obey, the compression of phase space that occurs in nonequilibrium molecular dynamics (NEMD) simulations is purely an artifact of the non-Hamiltonian equations of motion that arise in implementing the Evans-Hoover thermostat [53, 54]. (See Section VIIIC for a critical discussion of the NEMD method.) While the NEMD method is a valid simulation approach in the linear regime, the phase space compression induced by the thermostat awaits physical interpretation even if it does turn out to be related to the rate of first entropy production, then the hurdle posed by Question (3) remains to be surmounted. 

The vanishing of the second term in the optimum state arises from a cancelation that lends itself to a physical interpretation. This expression for the second entropy may be rearranged as... 

The most important new concept to come from thermodynamics is entropy. Like volume, internal energy and mole number it is an extensive property of a system and together with these, and other variables it defines an elegant self-consistent theory. However, there is one important difference entropy is the only one of the extensive thermodynamic functions that has no obvious physical interpretation. It is only through statistical integration of the mechanical behaviour of microsystems that a property of the average macrosystem, that resembles the entropy function, emerges. 

The above realization of the abstract mesoscopic equilibrium thermodynamics is called a Canonical-Ensemble Statistical Mechanics. We shall now briefly present also another realization, called a Microcanonical-Ensemble Statistical Mechanics since it offers a useful physical interpretation of entropy. 

We note that the classical equilibrium entropy (i.e., the eta-function evaluated at equilibrium states) acquires in the context of the Microcanonical Ensemble an interesting physical interpretation. The entropy becomes a logarithm of the volume of the phase space that is available to macroscopic systems having the fixed volume, fixed number of particles and fixed energy. If there is only one microscopic state that corresponds to a given macroscopic state, we can put the available phase space volume equal to one and the entropy becomes thus zero. The one-to-one relation between microscopic and macroscopic thermodynamic equilibrium states is thus realized only at zero temperature. 

To summarize, we have shown that a specific physical interpretation of the intensive variables governed by Equation (1.1) - temperature, pressure, and chemical potential - arises from the assumption that systems move to thermodynamic macrostates that maximize the number of accessible microstates. This is our first application of the famous second law of thermodynamics, which, as is implicit in the above derivations, is stated as the entropy of a closed system never decreases. It is worth noting that our interpretation of the intensive thermodynamic variables... 

Rational thermodynamics provides a method for deriving the constitutive equations without assuming local equilibrium. In this formulation, absolute temperature and entropy do not have a precise physical interpretation. It is assumed that the system has a memory, and the behavior of the system at a given time is determined by the characteristic parameters of both the present and the past. However, the general expressions for the balance of mass, momentum, and energy are still used. 

However, even though the application of the entropy equation in chemical reaction engineering is limited today, the understanding and physical interpretations of terms in the equation may be important in future process design and optimization . 

Mathematically, the BE distribution differs from the FD one just by a sign in the denominator, yet with deep consequences in the physical interpretation, as it will be seen below. We know that the determination of Lagrange parameters is based on the evaluation of entropy variation at the energy variation, in the absence of the variation of the total numbers of particles - for determination, respectively when the total number of particles slightly varies - for a determination. 

Dugdale, J.S. (1998). Entropy and its Physical Interpretation. Taylor Francis. ISBN 978-0-7484-0569-5. 

It is noted that (3.73) is equal to (3.65), which implies that the entropy production ds is caused by a non-measurable part of energy. Until now, no physical interpretation of entropy production has been given, but using the present framework makes it clear. This is the rationale for the development of this particular approach. ... 

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