**4. The first law and the second law of thermodynamics**

Theory of thermodynamics is constructed on the two laws of thermodynamics, the first law and the second law. Generally, students of thermodynamics consider that the first law is well understood but that the second law is the one that is difficult to comprehend. One obvious problem is that there are two versions of the second law: the original version formulated by Thomson (later, lord Kelvin) that of the universal degradation of mechanical energy [14], which'll be called, in short, *the energy principle*; the later version formulated by the Berlin School of thermodynamics by Clausius and Planck, which'll be called the entropy principle. The entropy principle has been universally acknowledged to be the true second law of thermodynamics.

There are multiple problems here. First is that though the entropy principle is accepted to be the true second law most students consider the meaning of the entropy principle to be encapsulated by the universal degradation of high-grade forms of energy, i.e., the energy principle. If the two principles are merely synonyms, that situation is acceptable. The problem worsens, therefore, because they are not. That demonstration can be made by showing that while the entropy principle is a universal principle, the energy principle is *not* a universal principle. Such a conclusion was reached by Planck [15]:

*The real meaning of the second law has frequently been looked for in a "dissipation of energy." This view, proceeding, as it does, from the irreversible phenomena of conduction and radiation of heat, presents only one side of the question. There are irreversible processes in which the final and initial states show exactly the same form of energy, e.g., the diffusion of two perfect gases or further dilution of a dilute solution. Such processes are accompanied by no perceptible transference of heat, nor by external work, nor by any noticeable transformation of energy. They occur only for the reason that they lead to an appreciable increase of the entropy ([5], pp. 103–104).*

Details of Planck's argument has been worked out in a recent book, *A Treatise of Heat and Energy* [16], which concludes that mechanical energy degrades spontaneously not universally.

A good question would be why Planck's conclusion, which is of supreme importance, has not been more widely disseminated. *A Treatise* seeks to explain this situation by arguing that the entropy principle formulated by the Berlin School was a selection principle: the 19th century Berlin School was under the sway of the foundationalist mechanical-philosophy and the only kind of selection permitted by the entropy principle as a selection principle in accordance with the mechanical philosophy is selection based on physical necessity or efficient causation. As a result of the metaphysics of necessity as physical necessity alone, the inevitability of entropy growth infers the corollary of inevitable accumulation of heat, i.e., the energy principle.

In short, under the sway of the mechanical-philosophy, Clausius and Planck were not able to formulate a second law that Planck clearly realized, later on, should cast away the energy principle.

Before a new formulation of the second law for achieving that purpose is discussed, let us look at the first law: it turns out that we have misconception about the first law as well. Misconception about the two laws is intrinsically intersected: The first law was based on the mechanical equivalent of heat, i.e., the equivalence principle. The equivalence principle is the idea that all forms of energy during transformation from one form to another are conserved, i.e., all energy-forms are universally connected. But connection does not mean (necessarily) causation. That misstep was taken by Thomson and Clausius when they independently formulated the first and the second laws by giving causal power (the power that should be the purview of the second law) to the first law—making it too powerful depriving the second law of its rightful purview. The result of that misstep is a second law as a selection principle instead of a selection and causal principle.

This point was made in A Treatise. A more detailed discussion can be found in a new paper [17]. Back to the issue on the second law: a short account of a new formulation of the second law as it is related to the Carnot cycle is shown here.

The Carnot cycle can be interpreted differently from how it has been taken according to the conventional perspective: Instead of it as "an energy conversion of heat energy at *TA* to mechanical energy," we consider the cycle as "the reversible event, in reference to a corresponding spontaneous event, of heat transfer from a *TA* hot body to a *TB* cold heat-reservoir." We thus begin, with the same setup enabling the Carnot cycle, by considering two "book-end" events,

1.The spontaneous event of the heat transfer process, the reference event, and

2.The reversible work production event of the Carnot cycle.

The book-end events define a *Poincare range* [15, 16]. Consider, first, entropy growth in the spontaneous event, in which the same amount of heat energy *QA* exiting the *TA* heat body enters the *TB* cold heat-reservoir. Therefore, the entropy growth in the universe is:

$$(\Delta\_{\rm G}\mathfrak{S})\_{univ} = \frac{-Q\_{\rm A}}{T\_A} + \frac{Q\_{\rm A}}{T\_B} \tag{3}$$

Whereas in the reversible event, a smaller amount of heat energy, *QB*, enters the *TB* cold heat-reservoir resulting in zero entropy growth, in accordance with the entropy principle,

$$0 = \frac{-Q\_A}{T\_A} + \frac{Q\_B}{T\_B} \tag{4}$$

The heat energies exchanged with the *TB* heat-reservoir during the two events are *QA* and *QA* ∙ *TB TA* , respectively, as summarized in **Table 1**.

Rather than as a fraction of *QA* in accordance with the conventional perspective, note, in this new perspective, that the mechanical energy, (*Wrev*), is *preciously* the


**Table 1.**

*Difference in heat discharged to heat-reservoir for the two book-end events.*

*difference* between the amounts of heat energy added to the *TB* heat-reservoir for the two events, given by:

$$W\_{rev} = Q\_A - Q\_A \bullet \frac{T\_B}{T\_A} \tag{5}$$

Which is found to be the product of the universe's entropy growth in the spontaneous event according to (3), ð Þ Δ*GS univ*, and the temperature of the cold heatreservoir, *TB*,

$$W\_{rev} = Q\_A - Q\_A \bullet \frac{T\_B}{T\_A} = T\_B \bullet \left(\frac{-Q\_A}{T\_A} + \frac{Q\_A}{T\_B}\right) = T\_B \bullet (\Delta\_G S)\_{univ} \tag{6}$$

Accordingly, we call the universe's entropy growth in the spontaneous event, ð Þ Δ*GS univ*, the "*entropy growth potential*" (EGP), ð Þ Δ*PS univ* (for the reason articulated in the paragraph below):

$$\left(\Delta\_{\rm G}\mathcal{S}\right)\_{\rm univ} = \left(\Delta\_{\rm P}\mathcal{S}\right)\_{\rm univ} \tag{7}$$

Eq. (6), then, becomes,

$$W\_{rev} = T\_B \bullet (\Delta\_P \mathbb{S})\_{univ} \tag{8}$$

The logic of calling ð Þ Δ*GS univ* "EGP" in (7) and (8) is that EGP is a *common property* (the term Poincare used in [16, 18]) of both events, as well as of all possible events in the Poincare range. This common property is the driver for enabling the *extraction* of a given amount of heat energy from the *TB* heat-reservoir and converting it to mechanical energy of the same amount; in each case the amount for a specific event, though subject to the same "common property," is different; the maximum amount of extracted heat for a Poincare range is given by (8).

The same kind of demonstration on the idea of a common property has been made for systems in general, especially for isolated composite systems, in A Treatise and in References [17, 19]. We have, therefore, as a new part of the second law, *entropy growth potential principle*, in a general statement [19]:

*for a given non-equilibrium system, the spontaneous event of the system approaching equilibrium state and the corresponding reversible event defined by the same initial and final states define its Poincare range; any event in the range shares the same common property of EGP, while the specific entropy growth is different dependent on the individual event in accordance with its individual causal necessity.*

Note that, for the existence of a system's EGP in association with change between the initial state and the final states of the system, physics does not require system energy change (though it often is associated with system energy change). Energy is NOT a necessary substrate for the existence of EGP. In contrast, physics (the second law) does require the system in its initial-state existence at nonequilibrium state. A good safe distance from equilibrium state is the defining condition for a system, any system, to be the driving force for making the world go around—the precise metric of which is its entropy growth potential, EGP.

In sum, the conventional formulation of the first law is too powerful depriving the second law, as a selection principle, of its rightful purview. We have reformulated the first law [17] by taking away the causal power of energy—and reformulated the second law [16, 19] as a selection principle (the inevitable growth of entropy) and causal principle (entropy growth potential principle).
