Negative Specific Heat Research Articles

Entropy and Negative Specific Heat of Doped Graphene: Topological Phase Transitions and Nernst's Theorem Revisited.

This study explores the thermodynamic properties of doped graphene using an adapted electronic spectrum. We employed the one-electron tight-binding model to describe the hexagonal lattice structure. The dispersion relation for graphene is expressed in terms of the hopping energies using a compositional parameter that characterizes the different dopant atoms in the lattice. The focus of the investigation is on the impact of the compositions, specifically the presence of dopant atoms, on the energy spectrum, entropy, temperature, and specific heat of graphene. The numerical and analytical results reveal distinct thermodynamic behaviors influenced by the dopant composition, including topological transitions, inflection points in entropy, and specific heat divergences. In addition, the use of Boltzmann entropy and the revision of Nernst's theorem for doped graphene are introduced as novel aspects.

Random Transitions of a Binary Star in the Canonical Ensemble.

After reviewing the peculiar thermodynamics and statistical mechanics of self-gravitating systems, we consider the case of a "binary star" consisting of two particles of size a in gravitational interaction in a box of radius R. The caloric curve of this system displays a region of negative specific heat in the microcanonical ensemble, which is replaced by a first-order phase transition in the canonical ensemble. The free energy viewed as a thermodynamic potential exhibits two local minima that correspond to two metastable states separated by an unstable maximum forming a barrier of potential. By introducing a Langevin equation to model the interaction of the particles with the thermal bath, we study the random transitions of the system between a "dilute" state, where the particles are well separated, and a "condensed" state, where the particles are bound together. We show that the evolution of the system is given by a Fokker-Planck equation in energy space and that the lifetime of a metastable state is given by the Kramers formula involving the barrier of free energy. This is a particular case of the theory developed in a previous paper (Chavanis, 2005) for N Brownian particles in gravitational interaction associated with the canonical ensemble. In the case of a binary star (N=2), all the quantities can be calculated exactly analytically. We compare these results with those obtained in the mean field limit N→+∞.

Cosmological observatories

Abstract We study the static patch of de Sitter space in the presence of a timelike boundary. We impose that the conformal class of the induced metric and the trace of the extrinsic curvature, K, are fixed at the boundary. We present the thermodynamic structure of de Sitter space subject to these boundary conditions, for static and spherically symmetric configurations to leading order in the semiclassical approximation. In three spacetime dimensions, and taking K constant on a toroidal Euclidean boundary, we find that the spacetime is thermally stable for all K. In four spacetime dimensions, the thermal stability depends on the value of K. It is established that for sufficiently large K, the de Sitter static patch subject to conformal boundary conditions is thermally stable. This contrasts the Dirichlet problem for which the region encompassing the cosmological horizon has negative specific heat. We present an analysis of the linearised Einstein equations subject to conformal boundary conditions. In the worldline limit of the timelike boundary, the underlying modes are linked to the quasinormal modes of the static patch. In the limit where the timelike boundary approaches the cosmological event horizon, the linearised modes are interpreted in terms of the shear and sound modes of a fluid dynamical system. Additionally, we find modes with a frequency of positive imaginary part. Measured in a local inertial reference frame, and taking the stretched cosmological horizon limit, these modes grow at most polynomially.

Fluid statics of a self-gravitating isothermal sphere of van der Waals' gas

We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravitating isothermal sphere with the van der Waals' thermodynamic model, whose equation of state features well-known terms that account for molecular attraction and size. The governing equations are formulated for any thermodynamic model with two intensive degrees of freedom, applied with the van der Waals' model and solved numerically in nondimensional form by finite-difference algorithms. After a brief summary of thermodynamic characteristics possessed by the van der Waals' model, and relevant to the present study, we proceed to the description of the results in terms of comparative graphs illustrating radial profiles of density, pressure, and gravitational field. We complement them with graphs that compare the dependence of central and wall densities on gravitational number for both perfect-gas and van der Waals' models and that attest dramatically and unequivocally how the presence of molecular-attraction and -size terms removes questionable fluid-statics results systematically found accompanying the perfect-gas model in standard treatments. We also describe, within a very brief and preliminary digression, how the sanitizing action of the mentioned terms affects the thermodynamics of the isothermal sphere by providing evidence of how the gravitational correction to entropy corresponding to the van der Waals' model makes sure that there is no risk of gravothermal catastrophes, negative specific heats, and thermal instabilities. Furthermore, we investigate the phenomenology related to self-gravitationally induced both liquid-gas phase equilibria and metastable-gas states and we describe how they arise naturally and self-consistently from the governing equations. We conclude with a summary of the main results and with a challenging proposal of future work meant to attempt a revalorization the perfect-gas model.

Specific heat of a driven lattice gas

Calorimetry for equilibrium systems aims to determine the available microscopic occupation and distribution of energy levels by measuring thermal response. Nonequilibrium versions are expected to add information on the dynamical accessibility of those states. We perform calculations on a driven exclusion process on an array of particle stations, confirming that expectation. That Markov model produces a fermionic nonequilibrium steady state where the specific heat is computed exactly by evaluating the heat fluxes that are entirely due to a change in ambient temperature. We observe a zero-temperature divergence (violation of the Third Law) when the Fermi energy and the kinetic barrier for loading and emptying become approximately equal. Finally, when the kinetic barrier is density-dependent, a stable low-temperature regime of negative specific heat appears, indicating an anti-correlation between the temperature–dependence of the stationary occupation and the excess heat.

Strong spin frustration and magnetism in kagomé antiferromagnets LnCu3(OH)6Br3 (Ln = Nd, Sm, and Eu)

To study the effects of lanthanide ions on the geometrically frustrated antiferromagnets and their magnetic properties, we grew high-quality single crystals of LnCu3(OH)6Br3 (Ln = Nd, Sm, and Eu) by hydrothermal method and studied their crystal structures and magnetic properties. The refinements of the crystal structure referred to the powder x-ray diffraction data show that LnCu3(OH)6Br3 adopt a Kapellasite-type layer structure, which is isostructural to their chlorine analogue. Magnetic susceptibilities demonstrate that LnCu3(OH)6Br3 have strong antiferromagnetic coupling and a pronounced magnetic frustration effect. Magnetization measurements indicate canted antiferromagnetic ordering of Cu2+ ions around 16 K within the kagomé plane and weak ferromagnetic coupling. Moreover, shoulder-like anomalies in specific heat around 16 K could be a signature of emergent of magnetic ordering. The low-temperature negative magnetization and specific heat of LnCu3(OH)6Br3 (Ln = Nd, Sm, and Eu) indicate that Ln 3+ ions induce more exotic magnetic ground state properties.

All About Polytropic Processes

Of all the conceivable ideal-gas processes, almost all introductory physics textbooks as well as more advanced texts on thermodynamics emphasize only four: isochoric, isobaric, isothermal, and adiabatic (isentropic). These are processes in which a state variable—volume, pressure, temperature, or entropy— remains constant. It turns out that these four processes are examples of a more general ideal-gas process, called a polytropic process, in which the specific heat remains constant. Polytropic processes are frequently discussed in engineering thermodynamics but rarely in physics. The goal of this paper is to bring polytropic processes to the attention of physics instructors. These processes have interesting properties (such as, in some cases, negative specific heat), they are easily accessible at the introductory physics level, and they expand the range of examples and problems that can be explored in thermodynamics.

Breakdown of the Migdal-Eliashberg theory and a theory of lattice-fermionic superfluidity

Superconductors become unstable at strong renormalized electron-phonon coupling which breaks the crystalline symmetry and gives rise to a new phase. Smoking-gun evidence for this instability is negative specific heat. The authors also predict an upper bound on the superconducting critical temperature and explain why and how a spurious lattice instability as a function of the bare electron-phonon coupling has been frequently mistaken for a genuine breakdown of the Migdal-Eliashberg theory.

Superconductivity near a quantum critical point in the extreme retardation regime

We study fermions at quantum criticality with extremely retarded interactions of the form $V(\omega_l)=(g/|\omega_l|)^\gamma$, where $\omega_l$ is the transferred Matsubara frequency. This system undergoes a normal-superconductor phase transition at a critical temperature $T=T_c$. The order parameter is the frequency-dependent gap function $\Delta(\omega_n)$ as in the Eliashberg theory. In general, the interaction is extremely retarded for $\gamma\gg 1$, except at low temperatures $\gamma>3$ is sufficient. We evaluate the normal state specific heat, $T_c$, the jump in the specific heat, $\Delta(\omega_n)$ near $T_c$, and the Landau free energy. Our answers are asymptotically exact in the limit $\gamma\to\infty$. At low temperatures, we prove that the global minimum of the free energy is nondegenerate and determine the order parameter, the free energy, and the specific heat. These answers are exact for $T\to0$ and $\gamma>3$. We also uncover and investigate an instability of the $\gamma$ model: negative specific heat at $T\to0$ and just above $T_c$.

Comments on the negative specific heat of the Toverline{T} deformed symmetric product CFT

We show that the Toverline{T} deformation of conformal field theories whose entropy grows as S(E) ∼ Eγ for γ > 1/2 exhibits negative specific heat in its microcanonical thermodynamic function S(ℇ). We analyze the large N symmetric product CFT as a concrete example of a CFT with this property and compute the thermodynamic functions such as S(ℇ) and ℇ(T). The negative specific heat in the microcanonical data is interpreted as signaling the first order phase transition when the system is coupled to a heat bath.

Synthesis, characterization of phosphate-based nano-mixtures of Fe and Ca and their thermal analysis

• Nano-scale mixtures of Fe and Ca have been synthesized. • Mixtures show endothermic behaviour. • Explanation of negative specific heat capacity. • Both mixtures show semiconductor behaviour due to very less bandgap, E g = 0.64 eV • Sensible energy storage materials. • Thermal energy storage. In this work, synthesis of two novel and economic mixtures, 0.6 F e 3 ( P O 4 ) 2 · 8 H 2 O · CaHP O 4 · 1.5 CaS O 4 · Ca ( OH ) 2 (FPC4B) and 0.6 F e 3 ( P O 4 ) 2 · CaHP O 4 · 1.5 CaS O 4 · 2 H 2 O · Ca ( OH ) 2 (FPC4A) in nano-scale have been reported. A simple chemical route (wet) was followed for the synthesis. ICP-OES and CHNS (Quantitative) were used to deduce the compositions. Several analytical techniques such as SEM, TEM, FT-IR, XRD, TG-DTA, UV-VIS-NIR, DSC have been used for the characterization of the mixtures. Analyses results revealed the structural confirmation and respective crystallite size of FPC4A (59.84 nm) and FPC4B (69.73 nm). Various functional groups present in the mixture were confirmed by FT-IR. The thermal stability of both mixtures was investigated by TG-DTA. DSC curve revealed endothermic behaviour of mixtures indicating that both FPC4A and FPC4B can be exploited as sensible heat storage materials. E g (bandgap) of both mixtures were found to be 0.64eV with a refractive index of 3·48. SEM and TEM revealed the topographic constraint of both mixtures, which is rod-like in appearance.

Thermodynamic instability of 3D Einstein-Born-Infeld AdS black holes * *Supported in part by the National Natural Science Foundation of China (11005016, 11875196, 11375121)

Super-entropic black holes possess finite-area but noncompact event horizons and violate the reverse isoperimetric inequality. It has been conjectured that such black holes always have negative specific heat at constant volume or negative specific heat at constant pressure whenever , making them unstable in extended thermodynamics. In this paper, we describe a test of this instability conjecture with a family of nonlinear electrodynamic black holes, namely 3D Einstein-Born-Infeld (EBI) AdS black holes. Our results show that when nonlinear electrodynamics effects are weak, the instability conjecture is valid. However, the conjecture can be violated in some parameter region when nonlinear electrodynamics effects are strong enough. This observation thus provides a counter example to the instability conjecture, which suggests that super-entropic black holes may be thermodynamically stable.

SYK wormhole formation in real time

We study the real time formation of the ground state of two coupled SYK models. This is a highly entangled state which is close to the thermofield double state and can be viewed as a wormhole. We start from a high temperature state, we let it cool by coupling to a cold bath. We numerically solve for the large N dynamics. Our main result is that the system forms a wormhole by going through a region with negative specific heat, taking time that is independent of N. The dynamics is smooth everywhere and it seems to follow the equilibrium thermodynamic configurations of the microcanonical ensemble. Also we comment on the relation between this coupled SYK model and Jackiw-Teitelboim gravity theory with bulk fields.

Phases of holographic interfaces

We compute the phase diagram of the simplest holographic bottom-up model of conformal interfaces. The model consists of a thin domain wall between three-dimensional Anti-de Sitter (AdS) vacua, anchored on a boundary circle. We distinguish five phases depending on the existence of a black hole, the intersection of its horizon with the wall, and the fate of inertial observers. We show that, like the Hawking-Page phase transition, the capture of the wall by the horizon is also a first order transition and comment on its field-theory interpretation. The static solutions of the domain-wall equations include gravitational avatars of the Faraday cage, black holes with negative specific heat, and an intriguing phenomenon of suspended vacuum bubbles corresponding to an exotic interface/anti-interface fusion. Part of our analysis overlaps with recent work by Simidzija and Van Raamsdonk but the interpretation is different.

Preface: Long-range interactions and synchronization

Spontaneous synchronization is a general phenomenon in which a large population of coupled oscillators of diverse natural frequencies self-organize to operate in unison. The phenomenon occurs in physical and biological systems over a wide range of spatial and temporal scales, e.g., in electrochemical and electronic oscillators, Josephson junctions, laser arrays, animal flocking, pedestrians on footbridges, audience clapping, etc. Besides the obvious necessity of the synchronous firings of cardiac cells to keep the heart beating, synchrony is desired in many man-made systems such as parallel computing, electrical power-grids. On the contrary, synchrony could also be hazardous, e.g., in neurons, leading to impaired brain function in Parkinson's disease and epilepsy. Due to this wide range of applications, collective synchrony in networks of oscillators has attracted the attention of physicists, applied mathematicians and researchers from many other fields. An essential aspect of synchronizing systems is that long-range order naturally appear in these systems, which questions the fact whether long-range interactions may be particular suitable to synchronization. In this context, it is interesting to remind that long-range interacting system required several adaptations from statistical mechanics \`a la Gibbs Boltzmann, in order to deal with the peculiarities of these systems: negative specific heat, breaking of ergodicity or lack of extensivity. As for synchrony, it is still lacking a theoretical framework to use the tools from statistical mechanics. The present issue presents a collection of exciting recent theoretical developments in the field of synchronization and long-range interactions, in order to highlight the mutual progresses of these twin areas.

Getting hotter by heating less: How driven granular materials dissipate energy in excess

We investigate how the kinetic energy acquired by a dense granular system driven by an external vibration depends on the input energy. Our focus is on the dependence of the granular behavior on two main parameters: frequency and vibration amplitude. We find that there exists an optimal forcing frequency, at which the system reaches the maximal kinetic energy: if the input energy is increased beyond such a threshold, the system dissipates more and more energy and recovers a colder and more viscous state. Quite surprisingly, the nonmonotonic behavior is found for vibration amplitudes which are sufficiently small to keep the system always in contact with the driving oscillating plate. Studying dissipative properties of the system, we unveil a striking difference between this nonmonotonic behavior and a standard resonance mechanism. This feature is also observed at the microscopic scale of the single-grain dynamics and can be interpreted as an instance of negative specific heat. An analytically solvable model based on a generalized forced-damped oscillator well reproduces the observed phenomenology, illustrating the role of the competing effects of forcing and dissipation.

Quantized Portfolio Theory

J.L. Kelly's maximization of single-period growth revealed an optimal allocation strategy, and exposed a hidden information rate. Ed Thorp continued and demonstrated how this allocation strategy could be applied to investment portfolios and coincidentally led straight to mean-variance optimization. This work investigates the implications of the growth/information-rate equivalence and reveals an unintuitive result --all trading signals must be binary. Trading on binary signals may seem too jarring to be practical, but expanding on this derived result reveals a portfolio theory that starts with maximizing expected growth, and ends with the use of data decompression and error correction codes to construct portfolios with optimal allocations. These procedures are able to smooth out discrete binary signals and fine-tune their allocations in a way that scales with confidence (as desired intuitively), and accomplishes this without degrading expectation of maximum capital growth. Pushing further into information theory and entropy, it's shown how the Brownian motion assumption of macroeconomic capital flows is fundamentally incorrect, and is actually the opposite --motion guided by negative specific heat, or anti Brownian motion. Through this examination, it remains very likely that the growth/information-rate equivalence discovered by J.L. Kelly may imply that the study of finance and economics may fundamentally be the study of computer science and thermodynamics.

Prethermalization with negative specific heat.

We study noncanonical relaxation in an aggregate of subsystems with negative specific heat. The Thirring instability drives the constituent subsystems towards the edges of their energy spectrum, so that the existence of a single adiabatic invariant results in structured noncanonical steady states that are spectacularly different from the grand-canonical prediction. For parameter regimes where this adiabatic invariance breaks down, the system exhibits prethermalization far away from integrability, with an unprecedented contrast between the prethermal- and thermal states.

Remarks on the thermodynamic stability of deformations

We point out that negative specific heat at high energies is a characteristic feature of many deformations, both in the original d = 2 case and in d = 1 quantum mechanical cousins. This paper is a contribution to the memorial volume in honor of P G O Freund.

Charged black holes in Einsteinian cubic gravity and nonuniqueness

Black holes are the simplest objects in the universe. They correspond to extreme deformations of spacetime geometry, and can exist even devoid of matter. In general relativity, (electro)vacuum black holes are uniquely determined by their mass, charge and angular momentum. This feature follows from a uniqueness theorem, which can be evaded if one considers higher dimensions or matter fields coupled to gravity. Here we find that Einsteinian cubic gravity, a well-motivated modification of Einstein gravity that includes third-order curvature corrections in accordance with low-energy effective theory expectations, admits black hole solutions with charge greater than mass, when minimally coupled to a Maxwell field. Moreover, we find that, in this regime, there can be two asymptotically flat black holes with the same charge and mass, posing the first example of vacuum black hole nonuniqueness in four dimensions that is free from pathologies. Examination of these black hole's thermodynamics reveals that when two branches coexist only the larger black hole is thermodynamically stable, while the smaller branch has negative specific heat. Einsteinian cubic gravity unveils two further surprising features. The charged black holes do not possess an inner horizon, in contrast with the usual Reissner-Nordstr\"om spacetime, thus avoiding the need to resort to strong cosmic censorship to uphold determinism. In addition to black holes, there exists a one-parameter family of naked singularity spacetimes sharing the same mass and charge as the former, but not continuously connected with them. These naked singularities exist in the under-extremal regime, being present even in pure (uncharged) Einsteinian cubic gravity.