Proving the Lorentz Invariance of the Entropy and the Covariance of Thermodynamics

The standard argument for the Lorentz invariance of the thermodynamic entropy in equilibrium is based on the assumption that it is possible to perform an adiabatic transformation whose only outcome is to accelerate a macroscopic body, keeping its rest mass unchanged. The validity of this assumption constitutes the very foundation of relativistic thermodynamics and needs to be tested in greater detail. We show that, indeed, such a transformation is always possible, at least in principle. The only two assumptions invoked in the proof are that there is at least one inertial reference frame in which the second law of thermodynamics is valid and that the microscopic theory describing the internal dynamics of the body is a field theory, with Lorentz invariant Lagrangian density. The proof makes no reference to the connection between entropy and probabilities and is valid both within classical and quantum physics. To avoid any risk of circular reasoning, we do not postulate that the laws of thermodynamics are the same in every reference frame, but we obtain this fact as a direct consequence of the Lorentz invariance of the entropy.

Study on the Expansion of Primary Flow for the Mixing Uniformity in the Two-Phase Ejector

The expansion of primary flow in the suction chamber of the CO2 two-phase ejector is investigated and its influences on the mixing characteristics are analyzed. An ejector model is developed, by constructing differential equations for mass, momentum and energy then get the governing equation. In the suction chamber, the expansion of primary flow and the compression of secondary flow are modeled along the flow path. Based on the constant-pressure mixing theory, the pressure equilibrium positions of two stream (namely at the inlet and inside of mixing chamber, respectively) are considered. The mass and energy transfer in the mixing chamber were analyzed by using the double-flow model formulation. The ejector performance parameters are obtained for the different operation conditions, and the distributions of temperature and velocity of two streams in the mixing chamber are presented. The simulation results showed the influence of primary flow expansion on the pressure lift ratio was relatively obvious, and the larger expansion distance was helpful to improve the mixing efficiency and decrease the thermodynamic entropy change during the mixing. Moreover, the temperature of secondary flow for lower primary flow pressure presented larger descent rates at the initial of mixing. This work is helpful for the improvement of ejector theoretical model and the optimization design.

Steady states of holographic interfaces

We find stationary thin-brane geometries that are dual to far-from-equilibrium steady states of two-dimensional holographic interfaces. The flow of heat at the boundary agrees with the result of CFT and the known energy-transport coefficients of the thin-brane model. We argue that by entangling outgoing excitations the interface produces thermodynamic entropy at a maximal rate, and point out similarities and differences with double-sided black funnels. The non-compact, non-Killing and far-from-equilibrium event horizon of our solutions coincides with the local (apparent) horizon on the colder side, but lies behind it on the hotter side of the interface. We also show that the thermal conductivity of a pair of interfaces jumps at the Hawking-Page phase transition from a regime described by classical scatterers to a quantum regime in which heat flows unobstructed.

How smooth is quantum complexity?

The “quantum complexity” of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational complexity, it has since been argued to hold a fundamental significance in its own right, as a physical quantity analogous to the thermodynamic entropy. In this paper, we present a unified perspective on various notions of quantum complexity, viewed as functions on the space of unitary operators. One striking feature of these functions is that they can exhibit non-smooth and even fractal behaviour. We use ideas from Diophantine approximation theory and sub-Riemannian geometry to rigorously quantify this lack of smoothness. Implications for the physical meaning of quantum complexity are discussed.

Landauer’s Principle a Consequence of Bit Flows, Given Stirling’s Approximation

According to Landauer’s principle, at least kBln2T Joules are needed to erase a bit that stores information in a thermodynamic system at temperature T. However, the arguments for the principle rely on a regime where the equipartition principle holds. This paper, by exploring a simple model of a thermodynamic system using algorithmic information theory, shows the energy cost of transferring a bit, or restoring the original state, is kBln2T Joules for a reversible system. The principle is a direct consequence of the statistics required to allocate energy between stored energy states and thermal states, and applies outside the validity of the equipartition principle. As the thermodynamic entropy of a system coincides with the algorithmic entropy of a typical state specifying the momentum degrees of freedom, it can quantify the thermodynamic requirements in terms of bit flows to maintain a system distant from the equilibrium set of states. The approach offers a simple conceptual understanding of entropy, while avoiding problems with the statistical mechanic’s approach to the second law of thermodynamics. Furthermore, the classical articulation of the principle can be used to derive the low temperature heat capacities, and is consistent with the quantum version of the principle.

Perturbed thermodynamics and thermodynamic geometry of a static black hole in f (R) gravity

In this paper, we consider a static black hole in [Formula: see text] gravity. We recapitulate the expression for corrected thermodynamic entropy of this black hole due to small fluctuations around equilibrium. Also, we study the geometrothermodynamics (GTD) of this black hole and investigate the adaptability of the curvature scalar of geothermodynamic methods with phase transition points of this black hole. Moreover, we study the effect of correction parameter on thermodynamic behavior of this black hole. We observe that the singular point of the curvature scalar of Ruppeiner metric coincides completely with zero point of the heat capacity and the deviation occurs with increasing correction parameter.

Area Entropy and Quantized Mass of Black Holes from Information Theory

In this paper, we present a derivation of the black hole area entropy with the relationship between entropy and information. The curved space of a black hole allows objects to be imaged in the same way as camera lenses. The maximal information that a black hole can gain is limited by both the Compton wavelength of the object and the diameter of the black hole. When an object falls into a black hole, its information disappears due to the no-hair theorem, and the entropy of the black hole increases correspondingly. The area entropy of a black hole can thus be obtained, which indicates that the Bekenstein–Hawking entropy is information entropy rather than thermodynamic entropy. The quantum corrections of black hole entropy are also obtained according to the limit of Compton wavelength of the captured particles, which makes the mass of a black hole naturally quantized. Our work provides an information-theoretic perspective for understanding the nature of black hole entropy.

Currencies in Resource Theories

How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like perfectly independent copies of states or exact knowledge of a quantum state. Here we introduce the general tool of “currencies” to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out. Currencies are a subset of resources chosen to quantify all the other resources—like Bell pairs in LOCC or a lifted weight in thermodynamics. We show that from very weak assumptions in the theory we can already find useful currencies that give us necessary and sufficient conditions for resource conversion, and we build up more results as we impose further structure. This work generalizes axiomatic approaches to thermodynamic entropy, work and currencies made of local copies. In particular, by applying our approach to the resource theory of unital maps, we derive operational single-shot entropies for arbitrary, non-probabilistic descriptions of resources.