Negative Specific Heat Research Articles

Critical dimension and negative specific heat in one-dimensional large- N reduced models

We investigate critical phenomena of the Yang-Mills (YM) type one-dimensional matrix model that is a large-$N$ reduction (or dimensional reduction) of the $D+1$ dimensional $U(N)$ pure YM theory (bosonic BFSS model). This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory. We study the matrix model at a three-loop calculation via the "principle of minimum sensitivity" and find that there is a critical dimension $D=35.5$: At $D \le 35$, the transition is of first order, while it is of second order at $D\ge 36$. Furthermore, we evaluate several observables in our method, and they nicely reproduce the existing Monte Carlo results. Through the gauge/gravity correspondence, the transition is expected to be related to a Gregory-Laflamme transition in gravity, and we argue that the existence of the critical dimension is qualitatively consistent with it. Besides, in the first order transition case, a stable phase having negative specific heat appears in the microcanonical ensemble, which is similar to Schwarzschild black holes. We study some properties of this phase.

Effective negative specific heat by destabilization of metastable states in dipolar systems.

We study dipolarly coupled three-dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath. In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low-energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems.

Signatures of Specific DNA Binding by the AT-Rich Interaction Domain of BAF250a.

The AT-rich interaction domain (ARID) containing BAF250a is a subunit of the BAF-A class of SWI/SNF chromatin remodeling complexes. The ARID belongs to a family of conserved DNA binding domains found in several eukaryotic proteins; however, its exact contribution to BAF250a function and the mechanism of its DNA binding are not well understood. Here we have probed the interaction of the BAF250a ARID with three different double-stranded DNA (dsDNA) sequences to understand its DNA binding properties. A comprehensive biophysical and thermodynamic study using nuclear magnetic resonance (NMR) spectroscopy and isothermal titration calorimetry revealed the complex nature of BAF250a ARID-DNA interactions. The thermodynamic signatures of the BAF250a ARID with 12 A-T bp dsDNA (AT-12) are distinct from those of 12 G-C bp dsDNA (GC-12) or 12 bp Dickerson dodecamer DNA (DD-12) sequences. We observed that the binding of the BAF250a ARID with AT-12 DNA is enthalpically driven in a tested temperature range of 5-25 °C. BAF250a ARID/AT-12 DNA interaction exhibited a larger negative calorimetric specific heat change (ΔCp) compared to that of BAF250a ARID/GC-12 DNA or BAF250a ARID/DD-12 DNA interactions. In the presence of salt (NaCl), ARID/AT-12 DNA binding was less perturbed than ARID/GC-12 DNA or ARID/DD-12 DNA binding. Overall, these results show that BAF250a ARID/AT-12 DNA interaction has signatures of "specific" binding. Furthermore, using NMR chemical shift perturbation experiments, we have identified DNA binding residues on the BAF250a ARID and generated a data-driven HADDOCK model of the ARID/DNA complex that was further supported by mutating key lysine residues that were found to be important for DNA binding.

Thermodynamic instabilities of generalized exotic BTZ black holes

We examine the conjecture that black holes violating the reverse isoperimetric inequality have negative specific heat at constant volume CV [1]. We test this conjecture on the family of generalized exotic Bañados, Teitelboim and Zanelli (BTZ) black holes and find that CV can be positive even when the reverse isoperimetric inequality is violated, providing a counter example to the conjecture. However in all cases where CV is positive, the specific heat at constant pressure CP is negative, indicating that generalized exotic black holes are thermodynamically unstable, suggesting that a broader version of the conjecture might hold.

Negative specific heat from non-planar interactions and small black holes in AdS/CFT

The gravity side of the gauge/gravity duality predicts the existence of small black holes with negative specific heat. A free theory of strings has a Hagedorn behavior, but it does not lead to negative specific heat. To understand such states one needs to consider a theory of interacting strings. In the dual gauge theory, the string interactions are related to non-planar diagrams. In this paper the simplest gauged matrix model of two free matrices, that has Hagedorn behavior is analyzed in detail. A simple double trace deformation of the Hamiltonian, proportional to the square of the free Hamiltonian is studied. If the interaction has a negative sign, mimicking a gravitational attraction, one produces states with negative specific heat perturbatively and one can still compute the equation of state relating the entropy and the energy. A more general argument based on non-planar interactions that are random and that grow faster in strength than the planar diagrams as a function of the planar energy suggests that states with negative specific heat appear generically.

Strongly coupled N=4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) in the strong coupling limit by using the AdS/CFT correspondence. The dual geometry is the rotating black 3-brane Type IIB supergravity solution with a single non-zero rotation parameter $r_{0}$ which sets a fixed mass scale corresponding to the scalar condensate $<\mathcal{O}>\,\,\sim r_{0}^4$ in the Coulomb branch. We introduce a new ensemble where $T$ and $<\mathcal{O}>$ are held fixed, i.e., the free energy $F(T,<\mathcal{O}>)$ is a function of $T$ and $<\mathcal{O}>$. We compute the equation of state (EoS) of $\mathcal{N} = 4$ cSYM at finite $T$, as well as the heavy quark-antiquark potential and the quantized mass spectrums of the scalar and spin-2 glueballs at $T=0$. By computing the Wilson loop (minimal surface) at $T=0$, we determine the heavy quark-antiquark potential $V(L)$ to be the Cornell potential, which is confining for large separation $L$. At $T\neq 0$, we find two black hole branches: the large black hole and small black hole branches. For the large black hole branch, that has positive specific heat, we find qualitatively similar EoS to that of pure Yang-Mills theory on the lattice. For the small black hole branch, that has negative specific heat, we find an EoS where the entropy and energy densities decrease with $T$. We also find a second-order phase transition between the large and small black hole branches with critical temperature $T_c=T_{min}$.

Thermodynamic properties of a long-range interacting Bose system in staggered magnetic field

This paper provides a brief introduction to the thermodynamic properties of long-range interaction Bose systems in the staggered magnetic field by using the microcanonical approach. The entropy, temperature, heat capacity, phase translation are analyzed separately, and we constructed global phase diagram of the system. First-order phase transition, second-order phase transition, and negative specific heat can be observed in such system.

Violation of the temperature-signifies-heat-flow rule in systems with long-range interactions.

For a long-range interacting spin chain model, the microcanonical ensemble predicts a region of negative specific heat and a temperature jump at the transition energy. After two similar long-range interacting subsystems of different size at different temperatures are weakly coupled, they exchange energy and the total microcanonical entropy of the full system increases irreversibly. The hot subsystem could spontaneously absorb heat from the cold subsystem via the thermal contact and the final equilibrium temperature could be lower than the initial temperatures of the cold subsystem. This result is confirmed by numerical simulations using the microcanonical Monte Carlo algorithm.

Thermodynamic analysis of a long-range interacting spin system

A long-range interacting Fermi chain placed in the uniform and the staggered magnetic field is studied via the micro-canonical approach. The relation between the entropy and the energy of the system is obtained by counting the number of microscopic states. We find that this system is non-ergodic and can exhibit first-order phase transition, second-order phase transition, or both. The microcanonical ensemble predicts negative specific heat regions and temperature jumps. Moreover, the global phase diagram of the system is constructed.

Towards non-AdS holography via the long string phenomenon

The microscopic description of AdS space obeys the holographic principle in the sense that the number of microscopic degrees of freedom is given by the area of the holographic boundary. We assume the same applies to the microscopic holographic theories for non-AdS spacetimes, specifically for Minkowski, de Sitter, and AdS below its curvature radius. By taking general lessons from AdS/CFT we derive the cut-off energy of the holographic theories for these non-AdS geometries. Contrary to AdS/CFT, the excitation energy decreases towards the IR in the bulk, which is related to the negative specific heat of black holes. We construct a conformal mapping between the non-AdS geometries and AdS3 × Sq spacetimes, and relate the microscopic properties of the holographic theories for non-AdS spaces to those of symmetric product CFTs. We find that the mechanism responsible for the inversion of the energy-distance relation corresponds to the long string phenomenon. This same mechanism naturally explains the negative specific heat for non-AdS black holes and the value of the vacuum energy in (A)dS spacetimes.

Dimensional regularization of Renyi’s statistical mechanics

We show that typical Renyi’s statistical mechanics’ quantifiers exhibit poles. We are referring to the partition function Z and the mean energy 〈U〉. Renyi’s entropy is characterized by a real parameter α. The poles emerge in a numerable set of rational numbers belonging to the α-line. Physical effects of these poles are studied by appeal to dimensional regularization, as usual. Interesting effects are found, as for instance, gravitational ones. In particular, negative specific heats.

Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence

The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence, seems to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non degeneracy assumptions on the associated $m$-vortex Hamiltonian, the $m$-point bubbling solutions of the mean field equation are non degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.

Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law.

In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system+ environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. Entropy and entanglement will be the main theme of our second paper on this subject matter.

Andreev reflections and the quantum physics of black holes

We establish an analogy between superconductor-metal interfaces and the quantum physics of a black hole, using the proximity effect. We show that the metal-superconductor interface can be thought of as an event horizon and Andreev reflection from the interface is analogous to the Hawking radiation in black holes. We describe quantum information transfer in Andreev reflection with a final state projection model similar to the Horowitz-Maldacena model for black hole evaporation. We also propose the Andreev reflection analogue of Hayden and Preskill's description of a black hole final state, where the black hole is described as an information mirror. The analogy between crossed Andreev reflections and Einstein-Rosen bridges is discussed: our proposal gives a precise mechanism for the apparent loss of quantum information in a black hole by the process of nonlocal Andreev reflection, transferring the quantum information through a wormhole and into another universe. Given these established connections, we conjecture that the final quantum state of a black hole is exactly the same as the ground state wave function of the superconductor/superfluid in the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity; in particular, the infalling matter and the infalling Hawking quanta, described in the Horowitz-Maldacena model, forms a Cooper pairlike singlet state inside the black hole. A black hole evaporating and shrinking in size can be thought of as the analogue of Andreev reflection by a hole where the superconductor loses a Cooper pair. Our model does not suffer from the black hole information problem since Andreev reflection is unitary. We also relate the thermodynamic properties of a black hole to that of a superconductor, and propose an experiment which can demonstrate the negative specific heat feature of black holes in a growing/evaporating condensate.

Ensemble inequivalence and absence of quasi-stationary states in long-range random networks

Ensemble inequivalence has been previously displayed only for long-range interacting systems with non-extensive energy. In order to perform the thermodynamic limit, such systems require an unphysical, so-called, Kac rescaling of the coupling constant. We here study models defined on long-range random networks, which avoid such a rescaling. The proposed models have an extensive energy, which is however non-additive. For such long-range random networks, pairs of sites are coupled with a probability decaying with the distance r as . In one dimension and with , the surface energy scales linearly with the network size, while for it is O(1). By performing numerical simulations, we show that a negative specific heat region is present in the microcanonical ensemble of a Blume–Capel model, in correspondence with a first-order phase transition in the canonical one. This proves that ensemble inequivalence is a consequence of non-additivity rather than non-extensivity. Moreover, since a mean-field coupling is absent in such networks, relaxation to equilibrium takes place on an intensive time scale and quasi-stationary states are absent.

The quasilinear theory in the approach of long-range systems to quasi-stationary states

We develop a quasilinear theory of the Vlasov equation in order to describe the approach of systems with long-range interactions to quasi-stationary states. The quasilinear theory is based on the assumption that, although the initial distribution is not Vlasov stable, nevertheless its evolution towards a Vlasov stable stationary state is such that it is always only slightly inhomogeneous. We derive a diffusion equation governing the evolution of the velocity distribution of the system towards a steady state. This steady state is expected to correspond to the space-averaged quasi-stationary distribution function reached by the Vlasov equation as a result of a collisionless relaxation. We compare the prediction of the quasilinear theory to direct numerical simulations of the Hamiltonian mean field model, starting from an unstable spatially homogeneous distribution, either Gaussian or semi-elliptical. In the Gaussian case, we find that the quasilinear theory works reasonably well for weakly unstable initial conditions (i.e. close to the critical energy ) and that it is able to predict the energy marking the effective out-of-equilibrium phase transition between unmagnetized and magnetized quasi-stationary states found in the numerical simulations. Similarly, the quasilinear theory works well for energies close to the instability threshold of the semi-elliptical case , and it predicts an effective out-of-equilibrium transition at . In both situations, the quasilinear theory works less well at energies lower than the out-of-equilibrium transition, the disagreement with the numerical simulations increasing with decreasing energy. In that case, we observe, in agreement with our previous numerical study (Campa and Chavanis 2013 Eur. Phys. J. B 86 170), that the quasi-stationary states are remarkably well fitted by polytropic distributions (Tsallis distributions) with index n = 2 (Gaussian case) or n = 1 (semi-elliptical case). In particular, these polytropic distributions are able to account for the region of negative specific heats in the out-of-equilibrium caloric curve, unlike the Boltzmann and Lynden-Bell distributions.

Specific heat anomaly in relaxor ferroelectrics and dipolar glasses

The temperature and electric field dependence of the specific heat of relaxor ferroelectrics and dipolar glasses is investigated by means of a Landau-type theoretical model. It is shown that the dipolar specific heat, which is due to the randomly interacting polar nanoregions in relaxors and electric dipoles in dipolar glasses, is negative in a temperature region below the permittivity maximum. Also, it follows that for sufficiently low values of the field, where the induced polarization shows a quasi linear field dependence, the dipolar specific heat is proportional to the second temperature derivative of the dielectric polarization. This quantity can be extracted from the experimental temperature profile of the polarization, thus enabling an indirect experimental estimate of the negative specific heat, which is demonstrated for a set of representative relaxor and dipolar glass systems.

Negative specific heat of black-holes from fluid-gravity correspondence

Black holes in asymptotically flat space-times have negative specific heat—they get hotter as they loose energy. A clear statistical mechanical understanding of this has remained a challenge. In this work, we address this issue using fluid-gravity correspondence which aims to associate fluid degrees of freedom to the horizon. Using linear response theory and the teleological nature of event horizon, we show explicitly that the fluctuations of the horizon-fluid lead to negative specific heat for a Schwarzschild black Hole. We also point out how the specific heat can be positive for Kerr–Newman or AdS black holes. Our approach constitutes an important advance as it allows us to apply the canonical ensemble approach to study thermodynamics of asymptotically flat black hole space-times.

Chaos in matrix models and black hole evaporation

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question ---especially aspects of this question such as a black hole's negative specific heat---we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large $N$ limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. Finally, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.

Phase transitions in Thirring’s model

In his pioneering work on negative specific heat, Walter Thirring introduced a model that is solvable in the microcanonical ensemble. Here, we give a complete description of the phase-diagram of this model in both the microcanonical and the canonical ensemble, highlighting the main features of ensemble inequivalence. In both ensembles, we find a line of first-order phase transitions which ends in a critical point. However, neither the line nor the point have the same location in the phase-diagram of the two ensembles. We also show that the microcanonical and canonical critical points can be analytically related to each other using a Landau expansion of entropy and free energy, respectively, in analogy with what has been done in (Cohen and Mukamel 2012 J. Stat. Mech. P12017). Examples of systems with certain symmetries restricting the Landau expansion have been considered in this reference, while no such restrictions are present in Thirring’s model. This leads to a phase diagram that can be seen as a prototype for what happens in systems of particles with kinematic degrees of freedom dominated by long-range interactions.