Teaching the third law of thermodynamics

This work gives a brief summary of major formulations of the third law of thermodynamics and their implications, including the impossibility of perpetual motion of the third kind. The last sections of this work review more advanced applications of the third law to systems with negative temperatures and negative heat capacities. The relevance of the third law to protecting the arrow of time in general relativity is also discussed. Additional information, which may useful in analysis of the third law, is given in the Appendices. This short review is written to assist lecturers in selecting a strategy for teaching the third law of thermodynamics to engineering and science students. The paper provides a good summary of the various issues associated with the third law, which are typically scattered over numerous research publications and not discussed in standard textbooks.Comment: 22 pages, 5 figure

Symmetric and antisymmetric forms of the Pauli master equation (for interaction of matter and antimatter quantum states)

When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter --- this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equi-balance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future.Comment: 12 pages, 2 figure

Intransitivity in Theory and in the Real World

This work considers reasons for and implications of discarding the assumption of transitivity, which (transitivity) is the fundamental postulate in the utility theory of Von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology, game theory, economics and competitive evolutionary dynamic. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e. approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems. Quantum preferences are also considered in the Appendix.Comment: 44 pages, 14 figures, 47 references, 6 appendice

One antimatter --- two possible thermodynamics

Conventional thermodynamics, which is formulated for our world populated by radiation and matter, can be extended to describe physical properties of antimatter in two mutually exclusive ways: CP-invariant or CPT-invariant. Here we refer to invariance of physical laws under charge (C), parity (P) and time reversal (T) transformations. While in quantum field theory CPT invariance is a theorem confirmed by experiments, the symmetry principles applied to macroscopic phenomena or to the whole of the Universe represent only hypotheses. Since both versions of thermodynamics are different only in their treatment of antimatter, but are the same in describing our world dominated by matter, making a clear experimentally justified choice between CP invariance and CPT invariance in context of thermodynamics is not possible at present. This work investigates the comparative properties of the CP- and CPT-invariant extensions of thermodynamics (focusing on the latter, which is less conventional than the former) and examines conditions under which these extensions can be experimentally tested.Comment: 20 pages, 4 figures. arXiv admin note: text overlap with arXiv:1209.198

Do we find hurricanes on other planets?

Vortices with intense rotation occur in nature at very different scales, with the bathtub vortex representing one of the smallest and atmospheric vortices – tornadoes, mesocyclones and cyclones – representing vortices of much greater scales. Large vortices have been also found in the atmospheres of other planets – the famous Jovian Great Read Spot (GRS), whose size exceeds the Earth diameter, has been observed for more than 300 years. Fujita [10] in his classical work on vortices in planetary atmospheres introduced a unified treatment of the vortical motion of different scales starting from a lab vortex (that is referred to here as a bathtub vortex) and finishing with the largest known vortex of GRS. The vortices were classified according to their scales, and vortical motions of this kind are viewed by Fujita as a truly universal feature of the nature. Modern science tends to view these vortices as completely different phenomena and has good reasons for this: the vortices are characterized not only by different scales but also by different levels of buoyancy, turbulence and axial symmetry present in the flow. Thus, although we cannot expect that any common approach can fully characterize the whole structure of these vortices, this does not eliminate the possibility of finding common explanations for certain features of the vortices. The term ”bathtub-like vortical flows” is used to characterize axisymmetric vortices with significant intensification of rotation at the center due to converging secondary motion present in the flow. We first give the overview of the theory which is based on asymptotic analysis of the evolution of vorticity in axisymmetric bathtub-like flows under assumptions of prime influence of the convective terms. If the axial vorticity is sufficiently strong, the bathtub-like flows are expected to be controlled by the compensating regime that prevents further increases of the relative rotation strength. We examine applicability of this theory to certain intermediate regions of large atmospheric vortices (tornadoes and hurricanes) and compare theoretical predictions with atmospheric measurements. We also discuss vortices observed on other planets