Abstract: The Kelvin formulation of the second law of thermodynamics permits the following generalization: If the efficiency of a heat engine approaches unity, then the rejected work vanishes. This generalization allows deriving the behavior of a Carnot cycle near absolute zero of temperature. Also, the unattainability of absolute zero can be shown. In turn, these results allow deriving the behavior of the entropy near absolute zero, as has already been shown previously. The point of view is the phenomenological, macroscopic, and non-statistical one of classical thermodynamics.

Abstract: Self-organizing open systems, sustained by continuous fluxes between sources and sinks, convert stochastic motion into structured efficiency, yet a first-principles explanation of this transformation remains elusive. We derive the time-dependent Average Action Efficiency (AAE)—defined as events per total action—from a stochastic–dissipative least-action principle formulated within the Onsager–Machlup and Maximum Caliber path-ensemble frameworks. The resulting Lyapunov-type identity links the monotonic rise of AAE to the variance of action and to the rate of noise reduction, delineating growth, saturation, and decay regimes. Self-organization emerges from a reciprocal feedback between dynamics and structure: the stochastic dynamics concentrates trajectories around low-action paths, while the resulting structure, through the evolving feedback precision parameter β(t), modulates subsequent dynamics. This self-reinforcing coupling drives a monotonic increase of the dimensionless Average Action Efficiency α_t =η/⟨ I⟩_t , providing a quantitative measure of organizational growth. In the deterministic limit, the theory recovers Hamilton’s Principle. The increase of AAE corresponds to a decrease in path entropy, yielding an information-theoretic complement to the Maximum Entropy Production and Prigogine–Onsager variational formalisms. The framework applies to open, stochastic, feedback-driven systems that satisfy explicit regularity conditions. In Part II, agent-based ant-foraging simulations confirm sigmoidal AAE growth, plateau formation, and robustness under perturbations. Because empirical AAE requires only event counts and integrated action, it offers a lightweight metric and design rule for feedback-controlled self-organization across physical, chemical, biological, and active-matter systems.

Abstract: Entropy appears in physics in many forms—thermal, quantum, informational, gravitational—yet its conceptual foundations remain disparate. We propose a unified definition of entropy grounded in global physical constraints. A constraint set C determines the admissible microstate region Γ(C), and the entropy is defined as S(C) = k_BlnVol[Γ(C)]. This constraint–volume formulation applies uniformly to classical and quantum systems, to internal and external degrees of freedom, and to finite or continuous state spaces, without invoking coarse-graining, ensembles, or subjective information. Local interactions generically weaken global constraints such as coherence, correlations, gradients, and entanglement structure. We prove a structural Second Law: whenever constraints decay under dynamical evolution, C(t +∆t) ⊆ C(t), the entropy must increase. This mechanism explains thermodynamic irreversibility, decoherence, thermalization, and hydrodynamic mixing as manifestations of constraint erosion, while identifying integrable and symmetry-protected systems as the exceptional cases in which constraints persist. The framework clarifies how macroscopic entropy can grow evenwhenmicroscopic dynamics are reversible, and why time itself is not a form of entropy. Classical thermodynamic entropy, quantum von Neumann entropy, and black hole entropy all emerge as special cases of the same structural principle.

Abstract:

The historical context of Szilard’s thought experiment is considered: Maxwell’s demon, Brownian motion, and naturalization of Maxwell’s demon by Smoluchowski. After that, the discussions of Szilard’s thought experiment in the second half of the 20th century are described: the penetration of information into statistical mechanics, the works of Brillouin, Bennett (Landauer’s principle) and Zurek. The second part of the paper is devoted to the criticism of thermodynamics of information. The critique of Earman and Norton is extended by considering levels of organization. Also, the problem of coordination with respect to information is discussed.

Abstract: In this paper, during the simulation analysis of a Curie phase transition shielding model, it was found that the cumulative mechanical work performed on a moving ferromagnet after one Curie phase transition cycle of the model is non-zero. Further analysis based on Curie phase transition theory and the thermodynamics of magnetic media indicates that after completing one phase transition cycle, the cumulative magnetization work on the Curie phase transition ferromagnet is zero, the internal energy of both the Curie ferromagnet and the entire model is conserved, yet mechanical work remains separately, which contradicts the conservation of energy. This discovery suggests that there are exceptions to the conservation of energy, and it is not absolute.

Abstract: This paper separately analyzes the thermodynamic processes of adiabatic superconducting phase transition in superconductors and adiabatic Curie phase transition in ferromagnets in magnetic fields. Through analysis, it is concluded that for an object undergoing a phase transition cycle, when the accumulated magnetization work is zero, the overall internal energy of the adiabatic phase transition system is conserved. However, in the model, the accumulated mechanical work done on the permanent magnet is not zero, which leads to non-conservation of energy in the model, contradicting the law of conservation of energy. This indicates that the law of conservation of energy also has exceptions and is not absolute.

Abstract: This paper introduces a Thermodynamic Unified Field Theory (UFT) where prime-enforced symmetry constraints emerge from helical recoils in photrino dynamics, unifying phase behaviors and transport phenomena through a covariant fugacity-Hessian equation. By deriving the viscous stress tensor from entropy maximization without pa-rameters, the framework resolves Navier-Stokes limitations (e.g., infinite speeds, non-Fourier transport) and reproduces empirical phase diagrams for substances like he-lium, water, and neon via prime-locked gears. We demonstrate how primes arise from triad indivisibility, leading to rational direction cosines that enforce shell uniformity and curvature floors. Applications to catalysis, superfluidity, and non-equilibrium systems highlight UFT's potential as a parameter-free TOE candidate, with time and gravity as emergent distortions in the flux sea.

Abstract: Using the concept of quantum wave probability, combined with the identity principle, we can derive the Boltzmann distribution, Fermi distribution, and Bose distribution. Different distributions correspond to different conditions. The Boltzmann condition corresponds to the Boltzmann distribution. The Fermi condition corresponds to the Fermi distribution. The Bose condition corresponds to the Bose distribution. This demonstrates that the foundation of these three statistical distributions is quantum wave probability, all originating from quantum mechanics. The Boltzmann distribution is also an independent quantum distribution and is not simply a sparse limit of the Fermi or Bose distributions. The essence of the Boltzmann distribution is a uniform distribution. The Fermi and Bose distributions are deviations from the uniform distribution. Particles that follow the Boltzmann distribution can be called Boltzmannons. Boltzmann entropy based on the quantum wave probability can resolve the Gibbs paradox. We need to rethink the fundamentals of statistical mechanics.

Abstract: The problem of coordination for thermodynamic entropy as a physical quantity is expressed in two related questions: 1) What counts as a measurement of entropy? 2) What is entropy? These issues are considered in this paper for thermodynamic properties of pure substances in classical thermodynamics. The conceptual model to define entropy in the second law of thermodynamics cannot be used directly to produce an ideal experiment related to real measurements. Thus, the solution of the problem of coordination for entropy is based on the tight integration of entropy with other thermodynamic properties in the formalism of classical thermodynamics. Therefore, the solution of the problem of coordination for entropy is related to the simultaneous solution of the problem of coordination for other thermodynamic quantities, such as heat capacity, internal energy, enthalpy, and the Gibbs energy.

Abstract: In his paper 'The Impossible Process: Thermodynamic Reversibility', John Norton criticized the concept of reversible processes in classical thermodynamics and suggested that they should be considered approximations. In mathematics, however, the term approximation is related to the approximately equal sign, which is inappropriate for the mathematical formalism of thermodynamics. This paper examines the relationship between the formalism of thermodynamics, conceptual models and the world, and then discusses Norton's proposal from this point of view. In conclusion, a proposal by mathematician Zorich for the reversible process of heat transfer between two bodies with different temperatures is described.

Abstract: This paper introduces a novel entropy formulation — multiplicative entropy — defined as the product of energy values across all units in a quantized homogeneous invariant network. Unlike traditional statistical entropy, this approach explicitly tracks irreversible energy redistribution pathways, offering an analytic and path-dependent description of entropy growth. Logarithmic transformation recovers classical entropy forms, while preserving temporal directionality and quantum-scale resolution. The model enables precise simulation of thermodynamic processes, supporting the development of Analytic Quantum Thermodynamics as a new framework for understanding entropy-driven dynamics. Crucially, the analytical multiplicative entropy formula proposed here responds to Planck’s long-sought vision of an entropy expression in analytic form, enabling the resolution of entropy to match the high resolution of quantum processes.

Abstract: Serrin’s works provided a new perspective on classical thermodynamics through his statements of the first law and the accumulation function, and of the second law and the accumulation theorem, as well as the subsequent result by Huilgol that the work done in a thermal cycle implies an inequality where the important temperatures of the thermal cycle and an integral similar to that of Clausius appear. Based on these pioneering works, explicit forms of the accumulation function have been derived for the Otto, Diesel, Stirling and Ericsson cycles. In this article, a straightforward alternative derivation is presented to obtain the inequality for the work done in a cycle, following the approaches of Serrin and Huilgol. The derivation of the accumulation function for the ideal air-standard Brayton cycle is provided, where the temperature constraints of the adiabatic compression and expansion processes under which it operates are analyzed. Finally, a practical example is presented to illustrate the application of Serrin’s accumulation function to the ideal air-standard Brayton cycle.

Abstract: Jos Uffink rejected the existence of the arrow of time in classical thermodynamics, and his views turned out to be influential in the philosophy of physics. However, this position omits the connection between classical thermodynamics and continuum mechanics and is based on a simplistic view of equilibrium states. In this article, this issue is discussed with an example of a temperature field; we examine the relationship between the Fourier heat equation and classical thermodynamics in the 19th century. With this example the relationship of the Clausius inequality to time and transport equations of continuum mechanics is clarified. The question is raised whether it makes sense to carry out the axiomatization of classical thermodynamics without continuum mechanics.

Abstract: The material–immaterial divide remains one of the deepest conceptual tensions in both science and philosophy. This paper introduces the Dual Entropy Uncertainty Frame-work (DEUF)—a quantitative, information-based model that unifies material structure and immaterial information under a single uncertainty law, SE × OE ≥ C. Structural Entropy (SE) and Optical Entropy (OE) represent complementary Shannon-type measures of configurational and informational uncertainty. Building upon the Hei-senberg Uncertainty Principle and Shannon Information Theory, DEUF provides a testable framework linking quantum duality, biological evolution, and Platonic ideal-ism. Empirical implications are outlined in terms of compensatory dynamics between structure and information. The framework resolves long-standing philosophical and scientific challenges and suggests that matter and information form a single, entropi-cally balanced continuum. The DEUF formulation opens a new path for studying en-tropy-driven self-organization and the informational basis of natural laws.

Abstract: Quantitative Geometrical Thermodynamics (QGT) exploits the entropic Lagrangian-Hamiltonian canonical equations of state as applied to entities obeying the holographic principle and exhibiting Shannon information, the creation of which measures the (validly defined) “entropic purpose” of the system. QGT provides a physical description for what we might consider the true ‘atoms’ of physical science, and has also recently enabled a number of significant advances: including accounting ab initio for the chirality of DNA and the stability of Buckminsterfullerene; the size of the alpha particle (and other nuclear entities) and the lifetime of the free neutron; and the shape, structure and stability of the Milky Way galaxy. All these entities, ranging in size over more than 38 orders of magnitude, can each be considered to be an ‘atom’; in particular, the size of the alpha is calculated from QGT by assuming that the alpha is a “unitary entity” (that is, than which exists no simpler). The surprising conclusion is that clearly compound entities may also be physically treated as unitary (“uncuttable”) according to a principle of scale relativity, where a characteristic size for such an entity must be specified. Since QGT is entropic, and is therefore described using a logarithmic metric (involving hyperbolic space), it is not surprising that the length scale must be specified in order to account for unitary properties and for an entity to be appropriately considered an ‘atom’. The contribution to physics made by QGT is reviewed in the context of the related work of others.

Abstract: The equilibrium between a sessile liquid droplet and its environment under gravity hold both theoretical significance and practical implications. However, debates regarding the existence of such equilibrium have persisted for decades. Here, the effects of gravity on liquid-gas systems are first analyzed, and the results show that the gravitational influence need not be included in the Kelvin equation. Then, by considering the changes in both the atmospheric pressure and the liquid surface curvature, a generalized Kelvin equation is derived. Using this generalized Kelvin equation rather than the simplified classical form, we show that sessile liquid droplets resting on a flat, horizontal solid surface can indeed achieve full equilibrium with their atmosphere even in the presence of gravity.

Abstract: The article considers the description of a macrosystem in terms that do not depend on the nature of the macrosystem. The results obtained can be used to describe macrosystem models of thermodynamic processes, and to create interdisciplinary models that take into account interactions of various nature. The macrosystem model is based on its representation in the form of a self-similar coloured oriented multigraph, for each node of which the equation of state is fulfilled, which connects extensive variables. One of the extensive variables is entropy, the maximum of which corresponds to the state of equilibrium. For processes in which fluxes are linearly dependent on driving forces, Onsager's relations are shown to be true, which makes it possible to prove that in the space of stationary processes, entropy production in a closed macrosystem is a metric similar to the Mahalanobis metric, which determines the distance between processes. Zero in such a space are reversible processes, thus the production of entropy shows the degree of irreversibility, as the distance from a researched process to a reversible one.

Abstract:

The emergence of the entropy-as-disorder metaphor in the 19th century is considered. The logic behind the emergence of the metaphor of negative entropy in Schrödinger’s book is presented. After that the irrelevance of the entropy-as-disorder metaphor as well as the negative entropy metaphor is discussed. An alternative metaphor based on the concept of free energy is proposed.

Abstract: In this work, we present a novel unified equation of state (UEOS) that integrates thermodynamic variables across all phases of matter, challenging longstanding paradigms in quantum mechanics and statistical physics. By deriving the UEOS from first principles combining relativistic invariance and nonlocal field interactions, we demonstrate that particle-wave duality emerges as an artifact of incomplete classical approximations rather than a fundamental property of quantum systems. Our analysis reveals those apparent dual behaviors in phenomena such as the double-slit experiment stem from emergent statistical fluctuations in the UEOS, effectively debunking the need for intrinsic duality and reconciling quantum observations with a purely field-theoretic framework. Furthermore, entropy is reinterpreted not as a measure of disorder but as a pseudo-thermodynamic quantity arising from incomplete knowledge of the UEOS parameters, resolving paradoxes in information theory and black hole thermodynamics. Finally, the UEOS elucidates the mystery of phase transitions by providing a continuous analytic function that predicts critical points without invoking symmetry breaking or renormalization group flows, offering exact solutions for van der Waals-like behaviors in real gases and superconductors. This unified approach not only simplifies the theoretical landscape but also suggests experimental tests via high-precision calorimetry and interferometry, paving the way for a paradigm shift in foundational physics.

Abstract: The second law of thermodynamics is grounded in our empirical experiences in which the total entropy of a physical system must always either increase or remain constant during any spontaneous process. This notion of entropy is classically described as a measure of the randomness or uncertainty concerning a system’s state and represents the degree to which the details of the system are unknowable and therefore unavailable to be converted into an identifiable activity or useful work. This uncertainty is a result of an observer’s inability to exactly discern, know, and predict the state of the system as a condition of indeterminacy. Recently, the concepts of entropy have been reconstituted as observational entropy corresponding to the observer’s lack of knowledge about the system. If the observer is to hold a central place in our modern understanding of en-tropy, then it is important to incorporate the biological principles for the processing of information as knowledge acquisition into the determination of these measures.