Vol 7 - Special issue LILA 3

Entropy: Thermodynamics – Energy – Environment – Economy

List of Articles

The review introduces a recently developed generalized nonequilibrium (NEQ) statistical thermodynamics, called Gen-Th and Gen-GSL-Th, having a mechanical foundation in which stochasticity is introduced but not the second law (SL) by following the Boltzmann-(Carnot-Clausius)-Gibbs-Maxwell (BCGM) proposal. Gen-Th is applicable to any system of any size in any arbitrary state, isolated or not, requires new techniques, clarifies various confusing points such as about generalized and exchange macroworks, and yielding many new results. Distinction between uniform and nonuniform deterministic Hamiltonians and their microstates, operationally defined internal variables and NEQ entropy S in an extended state space, and their temporal evolution are the new tools to formulate Gen-Th. By imposing mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics, we formulate a generalized second law (GSL), whose form (but not of SL) remains invariant for both positive and negative temperatures T . The entropy S provides an extension of the Carnot-Clausius approach to equilibrium (EQ) entropy. We clarify the concept of spontaneous processes for both positive and negative NEQ temperatures so that dS ≥ 0 forT >0 and dS < 0 forT < 0 without violating GSL/SL. We prove a no-go theorem for the impossibility of a violation of GSL/SL for spontaneous processes. Any violation of GSL/SL is due to nonspontaneous processes such as a creation of internal constraints that are not covered by GSL/SL. Some examples are given including metastable macrostates during vitrification for positive T . We end with some open problems, some of which are also relevant for glasses.

In this work, we provide a new proof of the uniqueness theorem for a family of entropy formulas including Shannon’s entropy. The conventional axiomatic structure, proposed by Shannon and Khinchin in their seminal work, is modified by using fewer assumptions and especially without using the axioms relative to thermodynamic entropy, i.e., the maximum of entropy corresponds to uniform probability distributions, or the entropy is an increasing function of the total number of states of a system, which are just part of the reasons for the kin relationship between the two notions.

The principle of maximum entropy (maxent) has been proposed as mathematical inferential method based on the subjectivity of probability distributions and of the associated information or entropy. In this work, we argue that, if we apply the fundamental principle of virtual work of mechanics to the random dynamics of thermodynamic systems, the vanishing virtual work on the whole system naturally yields equilibrium state maximizing thermodynamic entropy. This approach resonates with the objective view of entropy and the non-anthropocentric character of thermodynamics theory, and advocates considering maxent as a physical law governing the behaviors of entropy.

Present paper reports on a selective review of international works, and specifically those that have been published in International Journal of Thermal Sciences (previously Revue Générale de Thermique ). This review is the proof of the continuous interest for optimizations of thermomechanical engines but not only. We observe that numerous papers are concerned by other systems and processes, among them the ones devoted to reverse cycles machines (refrigerating machines, air conditioning, heat pump, cryogenics), but also thermochemical processes, fuel cells for example. Here we consider exclusively thermomechanical engines, and particularly Carnot engine. We revisit the modeling of thermomechanical engines, completed by extensions of the Carnot model in direction of the Chambadal modeling that focuses on the fundamental influence of heat transfer entropy, and entropy production through internal and external irreversibilities of the thermomechanical converter. This part remains original to our knowledge and gives up new results concerning first law efficiencies at maximum power, but also some more fundamental aspects: equipartition; minimum of entropy production; new concepts (action of entropy production related to time, or better said durations).

This article presents elements of technique and language for composing and performing with the Karlax digital musical instrument (DMI). Developed in the early 2010s, this interface is supported by an active community of composers/performers and an extensive repertoire. In this sense, the Karlax is an ideal candidate for a second phase of development with a DMI. Playing the Karlax or composing for this instrument requires a range of techniques and leads us to reconsider the place of instruments in the musical practices. To this end, the article offers a detailed examination of the interface, details different types of technique for composition and interpretation based on concrete examples, and proposes a philosophical and aesthetic framework, based on the main issues of sonic identity, the sound-gesture relationship, the interaction strategies and the perception.

Placed in the epistemological context of the Lîla Entropie project, the present communication reports and synthesizes the research published in Russian and in English by the authors seeking to enlarge the concept of space-time in fields of extended dimensions: complex time on the one hand and non-positive dimensional spaces on the other hand. It emerges from these studies that numerous properties which may appear paradoxical in standard models of physics (irreversibility of time, uncertainty principle, entanglement, expansion of the universe, emergence of living things) then appear as possible consequences of a mathematical order widen into these new dimensions. The link between these approaches and those of other contributors to lîla Entropy project should open up new insights with regard to the physics of complex systems. For additional informations, you can read the work of the same authors published under the title Anti Time and Anti Space by the Russian Academy of Sciences in 2016.

The decohering and collapsing process remains an open question in Quantum Mechanics. These processes are implicitly related to the possible arrow of time. The purpose of this article is to address these questions through the model ETH developed by Professor J. Fröhlich and his team at the Zurich. It will be noted that his model is not unrelated to the communications already published within the framework of the “Lîla-Entropie Project”, especially through the ordering of nested systems.