Universal validity of the second law of information thermodynamics

4 - The Second and Third Laws of Thermodynamics: Entropy

The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict and exhaustive formulation. In the previous article, it was shown that two of the three most famous thermodynamic formulations of the Second Law of Thermodynamics are non-exhaustive. However, the status of the statistical approach, contrary to common and unfounded opinions, is even more difficult. It is known that Boltzmann did not manage to completely and correctly derive the Second Law of Thermodynamics from statistical mechanics, even though he probably did everything he could in this regard. In particular, he introduced molecular chaos into the extension of the Liouville equation, obtaining the Boltzmann equation. By using the H theorem, Boltzmann transferred the Second Law of Thermodynamics thesis to the molecular chaos hypothesis, which is not considered to be fully true. Therefore, the authors present a detailed and critical review of the issue of the Second Law of Thermodynamics and entropy from the perspective of phenomenological thermodynamics and statistical mechanics, as well as kinetic theory. On this basis, Propositions 1-3 for the statements of the Second Law of Thermodynamics are formulated in the original part of the article. Proposition 1 is based on resolving the misunderstanding of the Perpetuum Mobile of the Second Kind by introducing the Perpetuum Mobile of the Third Kind. Proposition 2 specifies the structure of allowed thermodynamic processes by using the Inequality of Heat and Temperature Proportions inspired by Eudoxus of Cnidus's inequalities defining real numbers. Proposition 3 is a Probabilistic Scheme of the Second Law of Thermodynamics that, like a game, shows the statistical tendency for entropy to increase, even though the possibility of it decreasing cannot be completely ruled out. Proposition 3 is, in some sense, free from Loschmidt's irreversibility paradox.

In continuum physics, constitutive equations model the material properties of physical systems. In those equations, material symmetry is taken into account by applying suitable representation theorems for symmetric and/or isotropic functions. Such mathematical representations must be in accordance with the second law of thermodynamics, which imposes that, in any thermodynamic process, the entropy production must be nonnegative. This requirement is fulfilled by assigning the constitutive equations in a form that guaranties that second law of thermodynamics is satisfied along arbitrary processes. Such an approach, in practice regards the second law of thermodynamics as a restriction on the constitutive equations, which must guarantee that any solution of the balance laws also satisfy the entropy inequality. This is a useful operative assumption, but not a consequence of general physical laws. Indeed, a different point of view, which regards the second law of thermodynamics as a restriction on the thermodynamic processes, i.e., on the solutions of the system of balance laws, is possible. This is tantamount to assuming that there are solutions of the balance laws that satisfy the entropy inequality, and solutions that do not satisfy it. In order to decide what is the correct approach, Muschik and Ehrentraut in 1996, postulated an amendment to the second law, which makes explicit the evident (but rather hidden) assumption that, in any point of the body, the entropy production is zero if, and only if, this point is a thermodynamic equilibrium. Then they proved that, given the amendment, the second law of thermodynamics is necessarily a restriction on the constitutive equations and not on the thermodynamic processes. In the present paper, we revisit their proof, lighting up some geometric aspects that were hidden in therein. Moreover, we propose an alternative formulation of the second law of thermodynamics, which incorporates the amendment. In this way we make this important result more intuitive and easily accessible to a wider audience.

We have considered that the universe is the inhomogeneous (n+2)-dimensional quasi-spherical Szekeres space-time model. We consider the universe as a thermodynamical system with the horizon surface as a boundary of the system. To study the generalized second law (GSL) of thermodynamics through the universe, we have assumed the trapped surface is the apparent horizon. Next we have examined the validity of the generalized second law of thermodynamics on the apparent horizon by two approaches: i) using the first law of thermodynamics on the apparent horizon and ii) without using the first law. In the first approach, the horizon entropy has been calculated by the first law. In the second approach, first we have calculated the surface gravity and temperature on the apparent horizon and then the horizon entropy has been found from the area formula. The variation of internal entropy has been found by Gibb's law. Using these two approaches separately, we find the conditions for validity of GSL in the (n+2)-dimensional quasi-spherical Szekeres model.

In this work, we have considered a non-canonical scalar field dark energy model in the framework of flat FRW background. It has also been assumed that the dark matter sector interacts with the non-canonical dark energy sector through some interaction term. Using the solutions for this interacting non-canonical scalar field dark energy model, we have investigated the validity of generalized second law (GSL) of thermodynamics in various scenarios using first law and area law of thermodynamics. For this purpose, we have assumed two types of horizons viz apparent horizon and event horizon for the universe and using first law of thermodynamics, we have examined the validity of GSL on both apparent and event horizons. Next, we have considered two types of entropy-corrections on apparent and event horizons. Using the modified area law, we have examined the validity of GSL of thermodynamics on apparent and event horizons under some restrictions of model parameters.

Here, we investigate the growth of matter density perturbations as well as the generalized second law (GSL) of thermodynamics in the framework of f(R)-gravity. We consider a spatially flat FRW universe filled with the pressureless matter and radiation which is enclosed by the dynamical apparent horizon with the Hawking temperature. For some viable f(R) models containing the Starobinsky, Hu-Sawicki, Exponential, Tsujikawa and AB models, we first explore numerically the evolution of some cosmological parameters like the Hubble parameter, the Ricci scalar, the deceleration parameter, the density parameters and the equation of state parameters. Then, we examine the validity of GSL and obtain the growth factor of structure formation. We find that for the aforementioned models, the GSL is satisfied from the early times to the present epoch. But in the farther future, the GSL for the all models is violated. Our numerical results also show that for

Exergization

We propose Fisher information as a new calculable thermodynamic property that can be shown to follow the second and third laws of thermodynamics. However, Fisher information is qualitatively different from entropy and potentially possesses much more structure. Hence, a mathematical expression is derived for computing the Fisher information of a system of many molecules from the canonical partition function. This development is further illustrated through the derivation of Fisher information expressions for a pure ideal gas and an ideal gas mixture. Some of the unique properties of Fisher information are then explored through the classic experiment of the isochoric mixing of two ideal gases. Note that, although the entropy of isochorically mixing two ideal gases is always positive and is dependent only on the respective mole fractions of the two gases, the Fisher information of mixing has far more structure, involving the mole numbers, molecular masses, temperature, and volume. Although the application of Fisher information to molecular systems is clearly in its infancy, it is hoped that the present work will catalyze further investigation into a new and truly unique line of thought on thermodynamics.

Chapter 3 - Second and Third Law of Thermodynamics in open systems

The arrow-of-time phenomena are everywhere in the physical world, biological systems, and human society. Despite its great importance in physics, the second law of thermodynamics can only successfully explain small percentages of these arrow-of-time phenomena in the physical world, and generally not applicable in biology and human society. For example, the powerful second law of thermodynamics can neither explain arrow-of-time phenomena like Darwin’s evolution in biological systems, nor the globalization processes in human society. Most physicists regard the Darwinian evolution and human society as physical systems far away from thermodynamic equilibrium, which is a physics terminology means that the concept of entropy cannot be precisely defined and the second law of thermodynamics is not useful for studying the Darwinian evolution and human society. While the concept of equilibrium is one of the most important concepts in economics, the concept of equilibrium in economics and physics are two completely different concepts. This paper generalizes the second law of thermodynamics into a universal law of physics called law of equilibrium, which is universally applicable in any system governed by quantum mechanics including physical systems, biological systems, and human society. The concept of entropy in statistical physics is generalized using the concept of relative entropy or Kullback-Leibler divergence from the information theory. Law of equilibrium is one of five physics laws of social science, which is based on a new interpretation of quantum mechanics. In the framework of physics laws of social science, economics and other fields of social science become subfields of quantum physics. The concept of equilibrium and relative entropy are generalized to be equally applicable for all subfields of physics including biology and social science. Law of equilibrium provides a rock solid physics foundation to expand the traditional equilibrium analysis in economics and game theory into a universal mathematical framework useful to study social phenomena. This paper resolves two outstanding problems in modern physics: how to generalize the second law of thermodynamics to non-equilibrium physics, and the nature of arrow of time. This paper concludes that the irreversible processes and arrow of time phenomena in the physical world, biological systems, and human society are fundamentally the same quantum phenomena due to indeterministic nature of quantum events including human choices.

This study investigated the introduction of the second law of thermodynamics using the Legitimation Code Theory (LCT) (semantic waves) among first year chemistry students. The aim of the study was to investigate the extent LTC (semantic waves) reduce the entropy concept’s complexity and abstractness when introducing the second law of thermodynamics. A purposive sampling technique was used to sample participants from the accessible population. A sample of two hundred (n = 200) first-year chemistry students was chosen at a public university in South Africa. The study adopted a mixed-method research design. Data were collected using an Introductory Second Law of Thermodynamics Questionnaire (ISLTQ) and semi-structured interviews. Creating semantic waves during the lectures left many students in the trough of the sinusoidal wave of abstractness and complexity. Ranking the concepts related to entropy showed that many students knew the hierarchical order of the concepts. However, the interviews revealed that students tended to link entropy to the spread of particles instead of energy. The findings of this study are diagnostic and they assist module designers in determining the level of abstraction and complexity students face when introducing the second law of thermodynamics.
 
 Key words: Abstraction; complexity; Legitimation Code Theory; second law of thermodynamics; semantic waves.

As with the first law of thermodynamics, the second law of thermodynamics has been proven by countless examples. The Clausius statement of the second law of thermodynamics given in most of the literatures is “heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time”. After carefully studying Clausius’ mechanical theory of heat published from 1850 to 1865, we found that this is not true. Actually, Clausius already clearly stated that the second law of thermodynamics is “Theorem of the equivalence of the transformation of work to heat and the transformation of heat at a higher to a lower temperature”. The former statement is only a basic principle that can lead to the theorem of the equivalence of transformations. In addition, all processes in derivation of the theorem of the equivalence of transformations and proof of the equivalence between Clausius statement and Kelvin statement are reversible processes. The statement “Heat can never pass from a colder to a warmer body without some other change” only illuminates the spontaneous natural phenomenon in opposite direction that heat flows from high temperature to low temperature, which tells that heat at different temperatures are nonequivalent. Admittedly, Clausius discussed the process irreversibility and thereby obtained Clausius Inequality. But he only used the state change to measure the process irreversibility, which did not involve the concept of space, time and speed. Clausius just expressed that the process irreversibility will reduce heat efficiency and did not focus exclusively on the laws of process irreversibility. The misunderstanding of viewing Clausius statement as “Heat can never pass from a colder to a warmer body without some other change”, easily produces such a viewpoint that the second law of thermodynamics is the rule about process direction and irreversibility, consequently leading to the faulty assumption that the minimum entropy generation principle can be used to derive the transport law of heat conduction and optimize the heat transfer process. However, theory and practice analyses have proven that it is problematic. The action of heat conduction process is just half of entransy dissipation, whose variation points to the linear Fourier’s heat conduction law, which thereby has a better application for the optimization of heat transfer process. Transfer process has different laws from conversion process, so they should be treated distinguishingly and analyzed with different methods and indexes. It is not advisable to simply put heat transfer issues into category of non-equilibrium thermodynamics.

Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their applicability is limited, in particular when considering strong and continuous measurements. In this Letter, we overcome this shortcoming by deriving a novel fluctuation theorem, and the associated second law of information thermodynamics, which remain applicable in arbitrary feedback control scenarios. In our second law, the entropy production is bounded by the coarse-grained entropy production that is inferrable from the measurement outcomes, an experimentally accessible quantity that does not diverge even under strong continuous measurements. We illustrate our results by a qubit undergoing discrete and continuous measurement, where our approach provides a useful bound on the entropy production for all measurement strengths.

An alternative formulation of the second law of thermodynamics is presented in terms of twin systems in thermal equilibrium. This formulation allows a direct derivation of the thermodynamic variables of absolute temperature and entropy. The efficiency of Carnot cycles is also derived. Irreversible processes are defined in part two of the second law and the Kelvin-Planck and Clausius statements of the second law are derived.

Although the entropy of black holes in any diffeomorphism invariant theory of gravity can be expressed as the Wald entropy, the issue of whether the entropy always obeys the second law of black hole thermodynamics remains open. Since the nonminimal coupling interaction between gravity and the electromagnetic field in the general quadric corrected Einstein-Maxwell gravity can sufficiently influence the expression of the Wald entropy, we check whether the Wald entropy of black holes in the quadric corrected gravity still satisfies the second law. A quasistationary accreting process of black holes is first considered, which describes that black holes are perturbed by matter fields and eventually settle down to a stationary state. Two assumptions that the matter fields should obey the null energy condition and that a regular bifurcation surface exists on the background spacetime are further proposed. According to the two assumptions and the Raychaudhuri equation, we demonstrate that the Wald entropy monotonically increases along the future event horizon under the linear order approximation of the perturbation. This result indicates that the Wald entropy of black holes in the quadric corrected gravity strictly obeys the linearized second law of thermodynamics.