Bluff your way in the second law of thermodynamics

The aim of this article is to analyze the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-(a)symmetry and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Carath\'eodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-asymmetry plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. Key words: thermodynamics, second law, irreversibility, time-asymmetry, arrow of time.Comment: Studies in History and Philosophy of Modern Physics (to appear

Entropy? Exercices de Style

Since its inception, the concept of entropy has been known under a variety of guises and been used in an increasing number of contexts, achieving an almost rock star-like status in both the sciences and popular culture. The three most prominent “styles” which entropy has been (re)told in and which have determined its popularity are the thermodynamic, statistical and information-theoretic one, owing much to the work of Clausius, Boltzmann and Gibbs, and Shannon, respectively. In the relentless hunt for the core of the concept that spurred this development, connections with irreversibility and emergence of time, nature of probability and information emerged adding to its elusiveness as much as stimulating its proliferation and cross-contextual adoption. In this historical review, we retrace, through primary and secondary sources, the three main perspectives from which entropy has been regarded, emphasising the motivations behind each new version, their ramifications and the bridges that have been constructed to justify them. From this analysis of the foundations a number of characteristic traits of the concept emerge that underline its exceptionality as an engine of conceptual progress

The construction of Electromagnetism

Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture

The Science of ΘΔcs\Theta \Delta^{cs}

There is a long tradition of thinking of thermodynamics, not as a theory of fundamental physics (or even a candidate theory of fundamental physics), but as a theory of how manipulations of a physical system may be used to obtain desired effects, such as mechanical work. On this view, the basic concepts of thermodynamics, heat and work, and with them, the concept of entropy, are relative to a class of envisaged manipulations. This view has been dismissed by many philosophers of physics, in my opinion too hastily. This paper is a sketch and defense of a science of manipulations and their effects on physical systems. This is, I claim, the best way to make sense of thermodynamics as it is found in textbooks and as it is practiced. I call this science thermo-dynamics (with hyphen), or $\Theta \Delta^{cs}$, for short, to highlight that it may be different from the science of thermodynamics, as the reader conceives it. Even if one is not convinced that it is the best way to make sense of thermodynamics as it is practiced, it should be non-controversial that $\Theta \Delta^{cs}$ is a legitimate science. An upshot of the discussion is a clarification of the roles of the Gibbs and von Neumann entropies. Given the definition of statistical thermo-dynamic entropy, it can be proven that, under the assumption of availability of thermodynamically reversible processes, these functions are the unique (up to an additive constant) functions that represent thermo-dynamic entropy. Light is also shed on the use of coarse-grained entropies.

A Gradient Crystal Plasticity Theory Based on an Extended Energy Balance

An overview of different methods for the derivation of extended continuum models is given. A gradient plasticity theory is established in the context of small deformations and single slip by considering the invariance of an extended energy balance with respect to Euclidean transformations, where the plastic slip is considered as an additional degree of freedom. Thermodynamically consistent flow rules at the grain boundary are derived. The theory is applied to a two- and a three-phase laminate

The Science of ΘΔcs

There is a long tradition of thinking of thermodynamics, not as a theory of fundamental physics (or even a candidate theory of fundamental physics), but as a theory of how manipulations of a physical system may be used to obtain desired effects, such as mechanical work. On this view, the basic concepts of thermodynamics, heat and work, and with them, the concept of entropy, are relative to a class of envisaged manipulations. This view has been dismissed by many philosophers of physics, in my opinion too hastily. This paper is a sketch and defense of a science of manipulations and their effects on physical systems. This is, I claim, the best way to make sense of thermodynamics as it is found in textbooks and as it is practiced. I call this science thermo-dynamics (with hyphen), or \ΘΔcs, for short, to highlight that it may be different from the science of thermodynamics, as the reader conceives it. Even if one is not convinced that it is the best way to make sense of thermodynamics as it is practiced, it should be non-controversial that ΘΔcs is a legitimate science. An upshot of the discussion is a clarification of the roles of the Gibbs and von Neumann entropies. Given the definition of statistical thermo-dynamic entropy, it can be proven that, under the assumption of availability of thermodynamically reversible processes, these functions are the unique (up to an additive constant) functions that represent thermo-dynamic entropy. Light is also shed on the use of coarse-grained entropies