Clausius Entropy Research Articles

Interrelatedness of thermodynamics and information: transformation of heat as a measurable information process and quantity, an overview

AbstractNo one has yet investigated the information reach and influence of thermal analysis. Even so the heat and entropy are bound closely. The very problem of the term entropy is that it was defined specifically within the classical, equilibrium Thermodynamics like Clausius entropy, while its meaning is more general. It is usable in all areas of physics, in the communication theory and technology, and also, in social sciences, just as an universal quantitative model. The bridge to this wider world is in Boltzmann’s statistical point of view used in the Shannon’s information point of view. The difference is that the Shannon entropy is defined more generally, both for the uniform and for the not uniform probability distributions. But with renormalization and with the Boltzmann constant we can speak, using the Clausius entropy, about a certain thermodynamic system considered as a heat model of the area of our wider interests. So we will to deal with the heat and its entropy embodied to a wider consideration. In addition to the standard physical meaning, another thermodynamic realization in the form of a message is derived from Shannon’s information theory, where the sample carries a measure of Shannon’s information given by its structure or internal organization. This is also a contribution to improving the approach to thinking about the importance of observation and measurement, reflecting at the same time the costs and influence of the measurement itself and its organization on the measured object or, on its environment or, even on the environment of the measuring itself generally. Statistical sorting also carries with it the internal movement of individual elementary particles, the value of which indicates the resulting state of heat transfer and dissipation to and from the system providing a state of called equilibrium. It is statistically described by a weighted quantity called temperature, the changes of which via momentum alteration satisfy Newton’s laws of inertia allowing enumeration of the related heat information processing. The terminology used is still non-institutional.

Sensitivity of nonequilibrium relaxation to interaction potentials: Timescales of response from Boltzmann's H function.

We investigate, by simulations and analytic theory, the sensitivity of nonequilibrium relaxation to interaction potential and dimensionality by using Boltzmann's H function H(t). We evaluate H(t) for three different intermolecular potentials in all three dimensions and find that the well-known H theorem is valid and that the H function exhibits rather strong sensitivity to all these factors. The relaxation of H(t) is long in one dimension, but short in three dimensions, longer for the Lennard-Jones potential than for the hard spheres. The origin of the ultraslow approach to the equilibrium of H(t) in one-dimensional systems is discussed. Importantly, we obtain a closed-form analytic expression for H(t) using the solution of the Fokker-Planck equation for velocity space probability distribution and compare its predictions with the simulation results. Interestingly, H(t) is found to exhibit a linear response when vastly different initial nonequilibrium conditions are employed. The microscopic origin of this linear response is discussed. The oft-quoted relation of H function with Clausius's entropy theorem is discussed.

Thermoimpulse as a true extensive measure of heat

The expediency of replacing the Clausius entropy with a more adequate concept of "thermal impulse" as a measure of the amount of disordered motion in the system is substantiated. It is shown that the thermal impulse also exists in nonequilibrium systems, where it can also both increase and decrease. This makes it possible to solve the problem of thermodynamic inequalities, to return the concept of force to thermodynamics, to unify the methods for finding heterogeneous forces, to propose simpler criteria for the equilibrium, evolution and involution of each degree of freedom of the system separately, to substantiate the unity of the laws of transformation of any form of energy, to eliminate the blatant contradiction of thermodynamics with the nature of biological and cosmological evolution, etc. Other advantages of the thermal impulse are also revealed, which facilitate the proof of its existence, its applicability to thermally inhomogeneous media, physical visibility, measurability, ease of eliminating a number of paralogisms of thermodynamics, etc.

Air Source Super Heat Pumps That Extract Heat from the Air: the Law of Entropy Does Not Prohibit This

Electromobiles protect the biosphere in places of human residence. Globally, they destroy it, as the electrical energy they consumed is extracted using "dirty" energy carriers. This article suggests learning the electromobiles to generate electrical energy in eco-friendly way, extracting heat from the air. Specifically, we suggest to equip the electromobiles with the Or lov and etc. installation, which schematically is a converging tube where the air flow is by itself accelerated and, according to the Bernoulli equation, is cooled; and its narrow end contains the electrical energy generating turbine. The problem is that the Orlovand etc. installation is prohibited by the entropy increase law due to the flow entropy decrease during its operation. However, it is important that actually in this case the Clausius entropy, i.e. thermal entropy, decreases. The thermal and total entropy increase laws are different laws that separately require verification. Planck, Fermi et al. indicatedthe cases of total conversion of heat into other forms of energy accompanied by thermal en- tropy decrease. These cases, proving invalidity of the thermal entropy increase law, admit transition to electromobiles with air heat trac- tion. As well as transition of water transport to ship's electric engines with water heat traction.

Electric Vehicles That Extract Heat from the Air Without Charging: Entropy Law Does Not Prohibit This

Electromobiles protect the biosphere in places of human residence. Globally, they destroy it, as the electrical energy they consumed is extracted using "dirty" energy carriers. This article suggests learning the electromobiles to generate electrical energy in eco-friendly way, extracting heat from the air. Specifically, we suggest to equip the electromobiles with the Or lov and etc. installation, which schematically is a converging tube where the air flow is by itself accelerated and, according to the Bernoulli equation, is cooled; and its narrow end contains the electrical energy generating turbine. The problem is that the Orlovand etc. installation is prohibited by the entropy increase law due to the flow entropy decrease during its operation. However, it is important that actually in this case the Clausius entropy, i.e. thermal entropy, decreases. The thermal and total entropy increase laws are different laws that separately require verification. Planck, Fermi et al. indicatedthe cases of total conversion of heat into other forms of energy accompanied by thermal en- tropy decrease. These cases, proving invalidity of the thermal entropy increase law, admit transition to electromobiles with air heat trac- tion. As well as transition of water transport to ship's electric engines with water heat traction.

Entropy, the magic ruler?

The 18th century foundations of the second law of thermodynamics are discussed. The association between Carnot efficiency and Clausius entropy is described to show the questionable use of Clausius entropy as proof of Carnot’s assumption that the rate the ideal gas can convert heat energy to work between temperatures T1 and T2 sets a universal limit on the convertibility of heat to work by all 2T cyclical process.

Evolution of the universe from the perspective of entropy and information

Entropy is a key concept widely used in physics and other fields. At the same time, the meaning of entropy with different names and the relationship among them are confusing. In this paper, we discuss the relationship among the Clausius entropy, Boltzmann entropy and information entropy and further show that the three kinds of entropy are equivalent to each other to some extent. Moreover, we point out that the evolution of the universe is a process of entropy increment and life originates from the original low entropy of the universe. Finally, we discuss the evolution of the entire universe composed of the cosmological horizon and the space surrounded by it and interpret the entropy as a measure of information of all microstates corresponding to a certain macrostate. Under this explanation, the thermodynamic entropy and information entropy are unified and we can conclude that the sum of the entropy of horizon and the entropy of matter in the space surrounded by the horizon does not decrease with time if the second law of thermodynamics holds for the entire universe.

Quantum phenomenological gravitational dynamics: a general view from thermodynamics of spacetime

In this work we derive general quantum phenomenological equations of gravitational dynamics and analyse its features. The derivation uses the formalism developed in thermodynamics of spacetime and introduces low energy quantum gravity modifications to it. Quantum gravity effects are considered via modification of Bekenstein entropy by an extra logarithmic term in the area. This modification is predicted by several approaches to quantum gravity, including loop quantum gravity, string theory, AdS/CFT correspondence and generalised uncertainty principle phenomenology, giving our result a general character. The derived equations generalise classical equations of motion of unimodular gravity, instead of the ones of general relativity, and they contain at most second derivatives of the metric. We provide two independent derivations of the equations based on thermodynamics of local causal diamonds. First one uses Jacobson's maximal vacuum entanglement hypothesis, the second one Clausius entropy flux. Furthermore, we consider questions of diffeomorphism and local Lorentz invariance of the resulting dynamics and discuss its application to a simple cosmological model, finding a resolution of the classical singularity.

New perspective on thermodynamics of spacetime: The emergence of unimodular gravity and the equivalence of entropies

We present a novel derivation of Einstein equations from the balance between Clausius entropy crossing the boundary of a local causal diamond and entanglement entropy associated with its horizon. Comparing this derivation with the entanglement equilibrium approach developed by Jacobson, we are able to argue for the equivalence of matter entanglement and Clausius entropy in the semiclassical regime. We also provide a direct comparison of both entropies for conformal matter, showing their equivalence without appealing to gravitational dynamics. Furthermore, we determine that gravitational dynamics implied by thermodynamics of spacetime, in fact, corresponds to unimodular gravity rather than general relativity.

Thermal processes in natural gas pipeline transport

A commonly used premise in pipeline hydraulics where the work of friction forces performed at the movement of real gas in the gas pipeline completely turns into thermal energy is verified in the article. By means of the integral definition of Clausius entropy, it is shown that the premise of the conversion of friction forces into thermal energy of gas flow is justified with an acceptable accuracy for engineering applications in relation to the one-dimensional formulation of the task regarding the determination of the longitudinal temperature field of gas.

A Dynamical Systems-Based Hierarchy for Shannon, Metric and Topological Entropy

A rigorous dynamical systems-based hierarchy is established for the definitions of entropy of Shannon (information), Kolmogorov–Sinai (metric) and Adler, Konheim & McAndrew (topological). In particular, metric entropy, with the imposition of some additional properties, is proven to be a special case of topological entropy and Shannon entropy is shown to be a particular form of metric entropy. This is the first of two papers aimed at establishing a dynamically grounded hierarchy comprising Clausius, Boltzmann, Gibbs, Shannon, metric and topological entropy in which each element is ideally a special case of its successor or some kind of limit thereof.

Distinguishing between Clausius, Boltzmann and Pauling Entropies of Frozen Non-Equilibrium States.

In conventional textbook thermodynamics, entropy is a quantity that may be calculated by different methods, for example experimentally from heat capacities (following Clausius) or statistically from numbers of microscopic quantum states (following Boltzmann and Planck). It had turned out that these methods do not necessarily provide mutually consistent results, and for equilibrium systems their difference was explained by introducing a residual zero-point entropy (following Pauling), apparently violating the Nernst theorem. At finite temperatures, associated statistical entropies which count microstates that do not contribute to a body’s heat capacity, differ systematically from Clausius entropy, and are of particular relevance as measures for metastable, frozen-in non-equilibrium structures and for symbolic information processing (following Shannon). In this paper, it is suggested to consider Clausius, Boltzmann, Pauling and Shannon entropies as distinct, though related, physical quantities with different key properties, in order to avoid confusion by loosely speaking about just “entropy” while actually referring to different kinds of it. For instance, zero-point entropy exclusively belongs to Boltzmann rather than Clausius entropy, while the Nernst theorem holds rigorously for Clausius rather than Boltzmann entropy. The discussion of those terms is underpinned by a brief historical review of the emergence of corresponding fundamental thermodynamic concepts.

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction.

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies.

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Proc. R. Soc. 469, 20130408 (2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalization to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in nonequilibrium thermodynamics correspond to entropies used in one-shot information theory.

Self-organisation of symbolic information

Information is encountered in two different appearances, in native form by arbitrary physical structures, or in symbolic form by coded sequences of letters or the like. The self-organised emergence of symbolic information from structural information is referred to as a ritualisation transition. Occurring at some stage in evolutionary history, ritualisation transitions have in common that after the crossover, arbitrary symbols are issued and recognised by information-processing devices, by transmitters and receivers in the sense of Shannon's communication theory. Symbolic information-processing systems exhibit the fundamental code symmetry whose key features, such as largely lossless copying or persistence under hostile conditions, may elucidate the reasons for the repeated successful occurrence of ritualisation phenomena in evolution history. Ritualisation examples are briefly reviewed such as the origin of life, the appearance of human languages, the establishment of emergent social categories such as money, or the development of digital computers. In addition to their role as carriers of symbolic information, symbols are physical structures which also represent structural information. For a thermodynamic description of symbols and their arrangements, it appears reasonable to distinguish between Boltzmann entropy, Clausius entropy and Pauling entropy. Thermodynamic properties of symbols imply that their lifetimes are limited by the 2nd law.

Clausius entropy for arbitrary bifurcate null surfaces

Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation ) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations.

Clausius versus Sackur–Tetrode entropies

Based on the property of extensivity (mathematically, homogeneity of first degree), we derive in a mathematically consistent manner the explicit expressions of the chemical potential μ and the Clausius entropy S for the case of monoatomic ideal gases in open systems within phenomenological thermodynamics. Neither information theoretic nor quantum mechanical statistical concepts are invoked in this derivation. Considering a specific expression of the constant term of S, the derived entropy coincides with the Sackur–Tetrode entropy in the thermodynamic limit. We demonstrate, however, that the former limit is not contained in the classical thermodynamic relations, implying that the usual resolutions of Gibbs paradox do not succeed in bridging the gap between the thermodynamics and statistical mechanics. We finally consider the volume of the phase space as an entropic measure, albeit, without invoking the thermodynamic limit to investigate its relation to the thermodynamic equation of state and observables.

Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems

Recently, in their attempt to construct steady state thermodynamics (SST), Komatsu, Nakagawa, Sasa, and Tasaki found an extension of the Clausius relation to nonequilibrium steady states in classical stochastic processes. Here we derive a quantum mechanical version of the extended Clausius relation. We consider a small system of interest attached to large systems which play the role of heat baths. By only using the genuine quantum dynamics, we realize a heat conducting nonequilibrium steady state in the small system. We study the response of the steady state when the parameters of the system are changed abruptly, and show that the extended Clausius relation, in which “heat” is replaced by the “excess heat”, is valid when the temperature difference is small. Moreover we show that the entropy that appears in the relation is similar to von Neumann entropy but has an extra symmetrization with respect to time-reversal. We believe that the present work opens a new possibility in the study of nonequilibrium phenomena in quantum systems, and also confirms the robustness of the approach by Komatsu et al.

DSM-V and the Future of Suicidology

Classifications are an evolutionistic answer to individual generalizations. They are conceived to establish common grounds and shared languages, and to fight “natural” chaos. Especially from Rudolf Clausius (entropy) and Ludwig Boltzmann (statistical mechanics) have we learned that chaos can be triggered – in fact always is triggered – by strictly deterministic causes (Cardwell, 1971). We have also learned that, from a deterministic point of view, we can’t go on for more than three levels of physical interventions; after that we should be prepared to face the chaos. Incidentally, Boltzmann was a bipolar sufferer and a believer in a truly Darwinistic perspective for cultural evolution. He hanged himself in 1906, during a summer holiday near Trieste (which at the time belonged to the Austro-Hungarian empire). Suicidologists, neuroscientists, epidemiologists, mentalhealth professionals, and many more (not the least patients) will soon be challenged in their nosographic habits (or destinies) by the new versions of the International Classification of Diseases (ICD-11, to be released in 2015) and the Diagnostic and Statistical Manual of Mental Disorders (DSM-V, expected to be released in early 2013). The latter constitutes the focus of this editorial.

Moving Object Detection Based on Clausius Entropy

This paper proposes a novel image segmentation method based on Clausius entropy and adaptive Gaussian mixture model for detecting moving objects in a complex environment. The results suggest that the proposed method performs better than existing methods in extracting the foreground in various video sequences composed of multiple objects, lighting reflections, and background clutter.