Charge conservation, entropy current and gravitation

We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy–momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) timelike vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and Banãdos, Teitelboim and Zanelli (BTZ) black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein–Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.

Minimum Entropy Production Effect on a Quantum Scale

The discovery of quantized electric conductance by the group of van Wees in 1988 was a major breakthrough in physics. A decade later, the group of Schwab has proven the existence of quantized thermal conductance. Advancing from these and many other aspects of the quantized conductances in other phenomena of nature, the concept of quantized entropy current can be established and it eases the description of a transferred quantized energy package. This might yield a universal transport behavior of the microscopic world. During the transfer of a single energy quantum, hν, between two neighboring domains, the minimum entropy increment is calculated. It is pointed out that the possible existence of the minimal entropy transfer can be formulated. Moreover, as a new result, it is proved that this minimal entropy transfer principle is equivalent to the Lagrangian description of thermodynamics.

A case study of non-Fourier heat conduction using internal variables and GENERIC

Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s law and its various extensions—the Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys type, Ginzburg–Landau (Allen–Cahn) type and ballistic–diffusive heat conduction equations—are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.

An entropy current and the second law in higher derivative theories of gravity

We construct a proof of the second law of thermodynamics in an arbitrary diffeomorphism invariant theory of gravity working within the approximation of linearized dynamical fluctuations around stationary black holes. We achieve this by establishing the existence of an entropy current defined on the horizon of the dynamically perturbed black hole in such theories. By construction, this entropy current has non-negative divergence, suggestive of a mechanism for the dynamical black hole to approach a final equilibrium configuration via entropy production as well as the spatial flow of it on the null horizon. This enables us to argue for the second law in its strongest possible form, which has a manifest locality at each space-time point. We explicitly check that the form of the entropy current that we construct in this paper exactly matches with previously reported expressions computed considering specific four derivative theories of higher curvature gravity. Using the same set up we also provide an alternative proof of the physical process version of the first law applicable to arbitrary higher derivative theories of gravity.

General theory of large D membranes consistent with second law of thermodynamics

We write down the most general membrane equations dual to black holes for a general class of gravity theories, up to sub-leading order in 1/D in large D limit. We derive a “minimal” entropy current which satisfies a local form of second law from these membrane equations. We find that consistency with second law requires the membrane equations to satisfy certain constraints. We find additional constraints on the membrane equations from the existence of membrane solutions dual to stationary black holes. Finally we observe a tension between second law and matching with Wald entropy for dual stationary black hole configurations, for the minimal entropy current. We propose a simple modification of the membrane entropy current so that it satisfies second law and also the stationary membrane entropy matches the Wald entropy.

Non-boost invariant fluid dynamics

We consider uncharged fluids without any boost symmetry on an arbitrary curved background and classify all allowed transport coefficients up to first order in derivatives. We assume rotational symmetry and we use the entropy current formalism. The curved background geometry in the absence of boost symmetry is called absolute or Aristotelian spacetime. We present a closed-form expression for the energy-momentum tensor in Landau frame which splits into three parts: a dissipative (10), a hydrostatic non-dissipative (2) and a non-hydrostatic non-dissipative part (4), where in parenthesis we have indicated the number of allowed transport coefficients. The non-hydrostatic non-dissipative transport coefficients can be thought of as the generalization of coefficients that would vanish if we were to restrict to linearized perturbations and impose the Onsager relations. For the two hydrostatic and the four non-hydrostatic non-dissipative transport coefficients we present a Lagrangian description. Finally when we impose scale invariance, thus restricting to Lifshitz fluids, we find 7 dissipative, 1 hydrostatic and 2 non-hydrostatic non-dissipative transport coefficients.