Abstract: This paper introduces a novel framework for measuring entropy through tactile geometry, utilizing physical surface models to analyze complex systems. By extending the principles outlined in 'Tactile Geometry: A Structured Hypothesis of Skin Lines and Pore Function in Human Sensory Perception,' this study proposes that skin microstructures can serve as analogs for entropy distribution and conformal mapping. The approach offers a tangible method for visualizing and quantifying entropy, bridging thermodynamics and biological morphology to enhance our understanding of disorder and information flow in multifaceted systems.

Abstract: The main aim in this paper is to present new analytical representations of the thermodynamic functions of finite-temperature Thomas-Fermi model. First, an algorithm to solve the nonlinear equation of the model, which starts by rewriting it as a Fredholm integral equation, is described. Application of Newton's procedure, then, yields a sequence of linear Fredholm integral equations, which are solved using the standard Nystr{\"o}m's method. Use of Brachman's equation for direct computation of thermal energy of electrons is elaborated. Using extensive tabulations of the thermodynamic functions, over a wide range of scaled temperature and scaled densities, analytical representations of electron energy, pressure, ionization, Fermi energy and initial slope of Thomas-Fermi function are developed. Accuracy of these functions is established via computation of electron-Hugoniot and the Hugoniot of Cu and comparison with experimental (or theoretical) data up to about 20.4 TPa.

Abstract: I dispute the conventional claim that the second law of thermodynamics is saved from a "Maxwell's Demon" by the entropy cost of information erasure, and show that instead it is measurement that incurs the entropy cost. Thus Brillouin, who identified measurement as savior of the second law, was essentially correct, and putative refutations of his view, such as Bennett's claim to measure without entropy cost, are seen to fail when the applicable physics is taken into account. I argue that the tradition of attributing the defeat of Maxwell's Demon to erasure rather than to measurement arose from unphysical classical idealizations that do not hold for real gas molecules, as well as a physically ungrounded recasting of physical thermodynamical processes into computational and information-theoretic conceptualizations. I argue that the fundamental principle that saves the second law is the quantum uncertainty principle applying to the need to localize physical states to precise values of observables in order to effect the desired disequilibria aimed at violating the second law. I obtain the specific entropy cost for localizing a molecule in the Szilard engine, which coincides with the quantity attributed to Landauer's principle. I also note that an experiment characterized as upholding an entropy cost of erasure in a "quantum Maxwell's Demon" actually demonstrates an entropy cost of measurement.

Abstract: The Total Entropic Quantity (TEQ) framework derives quantum mechanics from entropy-driven selection principles, unifying entropy, emergent time, and thermodynamic evolution. TEQ decomposes total entropy into realized entropy (macroscopic disorder), latent entangled entropy (quantum correlations), and latent classical entropy (stable classical records), clarifying how classical irreversibility arises from global quantum coherence. A central result is \textit{Universal Entropic Time} (UET), defined by the monotonic growth of realized entropy. UET aligns the thermodynamic arrow of time with cosmological expansion, linking decoherence to macroscopic irreversibility. TEQ offers a unified epistemic-ontological interpretation of measurement, reconciling the Copenhagen and Many-Worlds views as complementary facets of entropy redistribution. It also provides an entropic explanation for quantum stability---especially in Majorana qubits---and suggests that spacetime and causal structure emerge from entropy gradients.TEQ yields two testable predictions: (1) Majorana qubits should exhibit extended coherence due to suppressed entropy flow; and (2) the entropic driver \(f(\Lambda(t))\) has a unique global maximum, implying that dark energy peaked in the past---a result consistent with recent DESI observations. Future work will derive quantum dynamics from an entropy-weighted variational principle, aiming to recover the Schr\"odinger equation, the Born rule, and quantum suppression from entropic constraints.

Abstract: We propose that a single irrational constant, ϕ≈1.618, serves as a universal attractor in far-from-equilibrium systems in a steady-state. In our Dynamic Balance framework, the dimensionless ratio α(t)=E˙(t)/T(t)S˙(t)—comparing the system’s energy throughput E˙ to its entropic heat loss TS˙—naturally converges to ϕ in a wide range of open, driven-dissipative processes. This ratio enforces a balance condition that partitions energy into useful work (order) and dissipative loss (disorder) in a way that maximizes both stability and adaptability. We demonstrate the principle using local cost functions, gradient-flow PDE expansions, Wilsonian renormalization group methods, and Markov master-equation analyses, showing in particular how it unifies near-critical behavior in the brain: the resulting neurodynamic PDE reproduces avalanche scaling, fractal wave expansions, short-term plasticity responses, and morphological growth patterns without ad hoc saturations. More broadly, the Dynamic Balance principle complements maximum entropy production and self-organized criticality in physics, parallels metabolic efficiency and fractal organization in biology, and implies optimal resource division in geology. We review empirical evidence—from stellar pulsations and fluid vortices to branching structures, quantum critical phenomena, and neural avalanche data—indicating that ϕ emerges as a robust signature of dynamic organization in non-equilibrium state-states.

Abstract: The review presents arguments emphasizing the importance of using the entropic measure of time (EMT) in the study of irreversible evolving systems. The possibilities of this measure for obtaining the laws of system evolution are shown. It is shown that EMT provides a novel and unified perspective on the principle of maximum entropy production (MEPP), which is established in the physics of irreversible processes, as well as on the laws of growth and evolution proposed in biology. Essentially, for irreversible processes, the proposed approach allows, in a certain sense, to identify concepts such as the duration of existence, MEPP, and natural selection. EMT has been used to generalize prior results, indicating that the intrinsic time of a system is logarithmically dependent on extrinsic (Newtonian) time.

Abstract:

Consider one particle (which could be an atom, molecule, Brownian particle, etc.) in thermodynamic equilibrium with a heat reservoir at temperature T. This particle can be in a low-potential-energy well L whose energy floor is E_L and whose degeneracy is G_L or in a higher (or at least equally high) potential-energy well H whose energy floor is E_H and whose degeneracy is G_H. L and H are separated by a barrier B, which the particle can traverse. The Second Law of Thermodynamics asserts that the ratio of the probability of this particle being in H to that of it being in L, i.e., the equilibrium constant K_eq corresponding to its dissemination between the two wells L and H, is in accordance with the Boltzmann (or canonical) distribution: K_eq = (G_H/G_L)exp[−(E_H – E_L)/kT]. Given thermodynamic equilibrium this indeed always obtains if transits between L and H occur only via thermal excitation of our particle. But we show that despite thermodynamic equilibrium this does not obtain if transits between L and H occur both via thermal excitation and via tunneling. Implications concerning the Second Law of Thermodynamics are discussed. Next, we provide general remarks pertaining to catalysis versus epicatalysis. Then we spotlight that only one aspect of the Second Law can challenged: the aspect thereof that precludes a net decrease in entropy. Following concluding remarks, the minimum work that the Second Law requires to change K_eq is evaluated in the Appendix.

Abstract: Simulation of transport properties of confined, low-dimensional fluids can be performed efficiently by means of Multi-Particle Collision (MPC) dynamics with suitable thermal-wall boundary conditions. We illustrate the effectiveness of the method by studying dimensionality effects and size-dependence of thermal conduction, properties of crucial importance for understanding heat transfer at the micro-nanoscale. We provide a sound numerical evidence that the simple MPC fluid displays the features previously predicted from hydrodynamics of lattice systems: (1) in 1D, the thermal conductivity $\kappa$ diverges with the system size $L$ as $\kappa\sim L^{1/3}$ and its total heat current autocorrelation function $C(t)$ decays with the time $t$ as $C(t)\sim t^{-2/3}$; (2) in 2D, $\kappa$ diverges with $L$ as $\kappa\sim \mathrm{ln} (L)$ and its $C(t)$ decays with $t$ as $C(t)\sim t^{-1}$; (3) in 3D, its $\kappa$ is independent with $L$ and its $C(t)$ decays with $t$ as $C(t)\sim t^{-3/2}$. For weak interaction (the nearly integrable case) in 1D and 2D, there exists an intermediate regime of sizes where kinetic effects dominate and transport is diffusive before crossing over to expected anomalous regime. The crossover can be studied by decomposing the heat current in two contributions, which allows for a very accurate test of the predictions. In addition, we also show that upon increasing the aspect ratio of the system, there exists a dimensional crossover from 2D or 3D dimensional behavior to the 1D one. Finally, we show that an applied magnetic field renders the transport normal, indicating that pseudomomentum conservation is not sufficient for the anomalous heat conduction behavior to occur.

Abstract: Consider one particle (which could be an atom, molecule, Brownian particle, etc.) in thermodynamic equilibrium with a heat reservoir at temperature T. This particle can be in a low-potential-energy well L whose energy floor is E_L and whose degeneracy is G_L or in a higher- (or at least equally high) potential-energy well H whose energy floor is E_H and whose degeneracy is G_H. L and H are separated by a barrier B, which the particle can traverse. The Second Law of Thermodynamics asserts that the ratio of the probability of this particle being in H to that of it being in L, i.e., the equilibrium constant Keq corresponding to its dissemination between the two wells L and H, is in accordance with the Boltzmann (or canonical) distribution: Keq = (G_H/G_L)exp[−(E_H – E_L)/kT]. Given thermodynamic equilibrium this indeed always obtains if transits between L and H occur only via thermal excitation of our particle. But we show that despite thermodynamic equilibrium this does not obtain if transits between L and H occur both via thermal excitation and via tunneling. Implications concerning the Second Law of Thermodynamics are discussed. We then provide general remarks pertaining to catalysis versus epicatalysis, followed by concluding remarks.

Abstract:

The local equilibrium approximation (LEA) is a central assumption in many applications of non-equilibrium thermodynamics involving the transport of energy, mass, and momentum. However, assessing the validity of the LEA remains challenging due to the limited development of tools for characterizing non-equilibrium states compared to equilibrium states. To address this, we have developed a theory based on kinetic theory, which provides a nonlinear extension of the telegrapher’s equation commonly discussed in non-equilibrium frameworks that extend beyond the LEA. A key result of this theory is a steady-state diffusion equation that accounts for the constraint imposed by available thermal energy on the diffusion flux. The theory is suitable for analysis of steady-state composition profiles and can be used to quantify the deviation from local equilibrium. To validate the theory, we performed molecular dynamics simulations. The results show that deviation from local equilibrium can be systematically quantified, and for the diffusion process we have studied here, we have confirmed that the LEA remains accurate even under extreme concentration gradients in gas mixtures.

Abstract:

In the previous work \cite{Aydiner_2024}, we presented a new interaction scheme that describes the interaction of thermodynamic systems. Using this interaction scheme, we showed that the interaction of dark matter and dark energy is chaotic. We also predicted that the results could be generalized to all particle and thermodynamic systems. In addition, we gave physical definitions of the concepts of chaos and self-organization. More importantly, we proposed a new law of physics based on interacting systems. Then, in this study, we considered two thermodynamic systems interacting under different conditions to prove the universality of the physical law we propose. We showed that these systems also have chaotic interaction dynamics. Furthermore, we discussed the physical and philosophical foundations of this new physics law and definition of chaos. In addition, we introduced a new action principle and a new complexity definition.

Abstract: Extremal principles of irreversible thermodynamics are considered, such as the principles of minimum and maximum entropy production in an analytically exactly solvable model of a Rayleigh gas with and without particle sources. It is shown that in an isolated system, during relaxation to an equilibrium state, the entropy production is minimal. In a system with sources, during relaxation of an equilibrium state to a nonequilibrium state, the entropy production is maximum. The concepts of free and forced the relaxation are introduced. Free relaxation is the transition of a system from a state far from equilibrium to a state close to equilibrium. Moreover, at each moment of relaxation, entropy production is minimal, i.e. the principle of minimum entropy production is fulfilled. During forced relaxation, the system moves from a state close to equilibrium to a state far from equilibrium, in which case the entropy production is maximum. It is shown that the principles of minimum and maximum entropy production are variational principles of irreversible thermodynamics under various thermodynamic conditions.

Abstract: In many technological processes, liquids or mixtures of mutually insoluble liquids, suspensions, emulsions, etc. are used as working media. The transformation of the energy supplied to such me-dia and the related effects can be usefully realised not only for the implementation of technological processes but also for their intensification. In this connection, an important task in increasing the efficiency of the use of the supplied energy is the analysis of the processes that take place in liquids or their mixtures at the level of thermodynamic saturation. In this work, it is shown that the crea-tion of thermodynamic conditions for local energy transformation in a disperse system signifi-cantly increases the intensity of heat and mass transfer processes, and in some technologies, e.g. homogenisation, dispersion can be increased by 2-3 times in comparison with traditional methods at the same energy consumption.

Abstract:

Purpose in systems is considered to be beyond the purview of science, since it is thought to be intrinsically personal. However, just as Claude Shannon was able to define an impersonal measure of information, so we formally define the (impersonal) ‘entropic purpose’ of an information system (using the theoretical apparatus of Quantitative Geometrical Thermodynamics) as the line integral of an entropic “purposive” Lagrangian defined in hyperbolic space across the complex temporal plane. We verify that this Lagrangian is well-formed: it has the appropriate variational (Euler-Lagrange) behaviour. We also discuss the teleological characteristics of such variational behaviour (featuring both thermodynamically reversible and irreversible temporal measures), so that a “Principle of Least (entropic) Purpose” can be adduced for any information-producing system. We show that entropic purpose is (approximately) identified with the information created by the system: an empirically measurable quantity. Exploiting the relationship between the entropy production of a system and its energy Hamiltonian, we also show how Landauer’s principle also applies to the creation of information; any purposive system that creates information will also dissipate energy. Finally, we discuss how ‘entropic purpose’ might be applied in artificial intelligence contexts (where degrees of system ‘aliveness’ need to be assessed), and in cybersecurity (where this metric for ‘entropic purpose’ might be exploited to help distinguish between people and bots).

Abstract: The concept of entropy, originally established in thermodynamics, serves as a cornerstone for understanding numerous physical phenomena. Commonly linked to disorder and the arrow of time, entropy has been extensively studied within the contexts of energy transfer and statistical mechanics. This paper proposes a novel interpretation of entropy through the lens of gravitational repulsion, offering a fresh perspective on its role in fundamental physics. By incorporating gravitational interactions, we aim to expand the conceptual framework of entropy and uncover new insights into its underlying principles.

Abstract:

Self-organizing criticalities are a much studied notion, within disciplines ranging from ecosystems/living systems to economic systems and markets. But there is still no consensus or general framework for explaining the ’spontaneous’ emergence of this kind of ’orderly’ behavior. This paper generalizes the second law of thermodynamics to dynamic state-spaces with increasing dimensionality and introduces the notion of spate-space curvature, in order to provide such a framework.

Abstract: There are currently four elementary forces in physics: gravity, electromagnetic force, and the weak and strong forces. In this paper, we propose a thermodynamic theory for gravity and show that the gravitational force is not an independent elementary force. We reveal that Newton’s gravitational force arises from microscopic thermodynamic potential energy. Additionally, we demonstrate that both Newton’s second law and the buoyancy force are also caused by this microscopic thermodynamic potential energy. Our calculation of the gravitational force shows a quantitative agreement with experimental data, offering a fresh perspective on gravity and buoyancy.

Abstract: The entropy production in the polarization phenomena occurring in the underlimiting regime, when an electric current circulates through a single cation-exchange membrane system, has been investigated in the 3-40 °C temperature range. From the analysis of the current-voltage curves and considering the electrolyte-membrane system as a unidimensional heterogeneous system, the total entropy generation in the system has been estimated from the contribution of each part of the system. Classical polarization theory and the irreversible thermodynamics approach have been used to determine the total electric potential drop and the entropy generation, respectively, associated with the different transport mechanisms in each part of the system. The results show that part of the electric power input is dissipated as heat due to both electric migration and diffusion ion transports, while another part is converted into chemical energy stored in the saline concentration gradient. Considering the electro-membrane process as an energy conversion process, an efficiency has been defined as the ratio between stored power and electric power input. This efficiency increases as both applied electric current and temperature increase.

Abstract: The status of the second law of thermodynamics, even in the 21st century, is not as certain as Arthur Eddington wrote about it a hundred years ago. However, it is not about the truth of this principle, but rather about its strict and exhaustive formulation. In the previous article it was shown that two of the three most famous thermodynamic formulations of the second law are non-exhaustive. However, the status of the statistical approach, contrary to common and unfounded opinions, is even more difficult. Well, it is known that Boltzmann did not manage to fully derive the second law from statistical mechanics, even though he did probably everything possible in this regard. In particular, he introduced deterministic chaos into the Liouville equation, obtaining the Boltzmann equation. Using the H theorem, Boltzmann transferred the second law thesis to the molecular chaos hypothesis, which is not considered to be fully true. Therefore, the authors presented a detailed and critical review of the issue of the second law of thermodynamics and entropy from the perspective of phenomenological thermodynamics and statistical mechanics. On this basis, Propositions 1–3 for the second law of thermodynamics were formulated in the original part of the article. It has been proven that Propositions 1–2 in thermodynamic terms are equivalent to the full entropic formulation of the second law. And the probabilistic approach to Proposition 3 was delivered directly. It has been argued that Proposition 3 is in some sense free from Loschmidt’s irreversibility paradox.

Abstract: A new analytical expression is proposed for the reduced influence parameter in Density Gradient Theory when combined with the Peng-Robinson equation of state for 32 n-alkanes. It contains the critical and triple point temperature values for each fluid as input and three adjustable coefficients. The new analytical expression contains the two-coefficients Zuo and Stenby and Miqueu et al.correlations as particular cases, and it is a modification of the previously published Cachadiña et al. correlation. Initially, the correlation coefficients for each fluid were obtained by fitting selected values for surface tension, and the results were comparable to other specific correlations reported in the literature. The overall mean absolute percentage deviation (OMAPD) between the selected and calculated data is just 0.79% Then, a general correlation including six adjustable coefficients valid for all the considered n-alkanes is proposed. It includes the radius of gyration as a new input parameter for each fluid. In this case, the OMAPD is 1.78\%. The use of other fluid properties as inputs is also briefly discussed.