Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

The paper studies constitutive modelling of Korteweg fluids. Thermodynamic consistency, i.e. compatibility with entropy balance law, is achieved using Liu's method of multipliers. Appropriate constitutive assumptions facilitated inclusion of the capillary effects in the specific entropy. Korteweg stresses are derived from the equilibrium conditions – vanishing of the entropy production and its minimization in equilibrium. Material parameter in Korteweg stresses is allowed to depend on temperature, which turns out to be consistent with kinetic-theory results and leads to cross-coupling of mechanical and thermal effects. The generalized Gibbs' relation, which inherits the capillary effects, is derived as consequence, which is a peculiar feature of the Liu's method.

The thermodynamic basis of classical mechanics is presented. In this framework, ideal Newtonian mechanics emerges as the zero-dissipation limit of a more general, dissipative theory. The thermodynamic approach predicts a novel dissipative contribution to the momentum that depends on the applied force, leading to a damping coefficient with a specific, experimentally testable dependence on the inertial mass and the spring constant. A torsion balance experiment with variable moment of inertia has been designed to measure this effect. Several known equations, including a thermodynamic version of the Eliezer-Ford-O'Connell equation of radiation reaction, are recovered as special cases.

In a recent work, Somogyfoki et al. (J. Non-Equilib. Thermodyn. vol. 50, pp. 59-76, 2025) analysed the linear stability of homogeneous equilibrium in third-order non-Fourier heat conduction within the framework of non-equilibrium thermodynamics with internal variables. They identified a stability condition, their equation (49), which could not be derived from the standard thermodynamic inequalities for the 2 & times; 2 conductivity blocks, and concluded that the Second Law does not guarantee stability in the most general case. Here we show that this conclusion was due to an overly conservative proof strategy: the standard thermodynamic conditions (concave entropy and non-negative entropy production, as expressed by the 2 & times; 2 block positive-definiteness inequalities (19)-(20) of the original paper) do suffice for linear stability. The key observation is that all coefficients of the dispersion polynomial remain positive for all physical wave numbers because their structure prevents positive real roots. This result confirms that thermodynamics, understood as a stability theory (V & aacute;n, Phil. Trans. R. Soc. A, vol. 381, 2023, Art. no. 20220276), ensures fundamental dynamic stability in all thermodynamically consistent third-order extended heat conduction theories. A comparison with the rate-equation approach of Giorgi, Morro and Zullo (Meccanica, vol. 359, pp. 1757-1776, 2024) is also presented.

Since black holes lack a straightforward notion of geometrical volume due to their event horizon structure and coordinate dependence, various approaches have been proposed to introduce a meaningful geometric and thermodynamic volume. In this work, we investigate the stability conditions of AdS black holes with and without volume.

A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations for the pressure tensor and energy current density are determined by the Liu procedure. Classical holography of perfect (non-dissipative) fluids is generally proven, according to which the divergence of the pressure tensor can be given by the gradient of a corresponding scalar potential. A consequence of holographic property is vorticity conservation, which opens the way toward wave-function representation of hydrodynamic equations to obtain the Schrödinger equation. Another special case of the derived fluid model is Newtonian gravity, when the internal variable is the gravitational potential itself. Coupled phenomena, such as the Schrödinger–Newton system, are also discussed. The presented thermodynamic framework can shed light on some connections between formulations of classical and quantum physics.

In this note we compare the entropy principle and the objectivity arguments in the methodologies of Dunn and Serrin [1] and in the more recent weakly nonlocal thermodynamic analysis of Korteweg-type fluids in [2]. It is concluded that the different objectivity approaches lead to the same constitutive functions, and that the difference in the thermodynamically compatible pressure tensors of perfect Korteweg fluids is due to different symmetry requirements.

Since black holes lack a straightforward notion of geometrical volume due to their event horizon structure and coordinate dependence, various approaches have been proposed to introduce a meaningful geometric and thermodynamic volume. There is no volume in classical black hole thermodynamics, the nonextensivity of black holes is a consequence. Extensivity of such systems can be restored by introducing a new thermodynamic state variable, typically the volume, the mass or the number of particles. Smarr relations show that black hole thermodynamics is nonextensive. However, restored extensivity leads to a volume which corresponds to geometric concepts and is also meaningful from a physical point of view. The article examines various volume definitions in the context of Anti-de Sitter (AdS) black holes and their implications for phase transitions, focusing on the Hawking-Page transition in Kerr-AdS spacetime, including the Christodoulou-Rovelli volume.

The fundamental dynamic stability of heat conduction theories beyond Fourier is analyzed in the framework of nonequilibrium thermodynamics. It is shown, that the thermodynamic framework, concave entropy and nonnegative entropy production, can ensure the stability of homogeneous thermodynamic equilibrium. Various special heat conduction theories of Extended Thermodynamics are compared and analysed in the general framework.

The stability of homogeneous thermodynamic equilibrium is analyzed in heat conduction theories in the framework of nonequilibrium thermodynamics, where the internal energy, the heat flux and a second order tensor are thermodynamic state variables. It is shown, that the thermodynamic conditions of concave entropy and nonnegative entropy production can ensure the linear stability. Various special heat conduction theories, including Extended Thermodynamics, are compared in the general framework.

The backbone of non-equilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and stable ones survive. The physical concepts from the stability structure and the related formalism of constrained entropy inequality are universal by construction. Therefore, the mathematical tools and the physical concepts of thermodynamics help formulate dynamical theories of any systems in social and natural sciences. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

Quantum mechanics, superfluids, and capillary fluids are closely related: It is thermodynamics that links them. In this paper, the Liu procedure is used to analyze the thermodynamic requirements. A comparison with the traditional method of divergence separation highlights the role of spacetime. It is shown that perfect Korteweg fluids are holographic. The conditions under which a complex field can represent the density and velocity fields of the fluid, and where the complex scalar field becomes a wave function of quantum mechanics, are explored. The bridge between the field and particle representations of a physical system is holography, and the key to holography is the Second Law of Thermodynamics.

More than 30 minutes before the earthquake event in Florina, Greece at 21:43:47(UTC) on 9th January 2022 an enhanced Eötvös torsion balance registered unidentified signals in the Jánossy Underground Research Laboratory in Budapest, Hungary. These signals were not visible on the seismograms, although seismic noises are continuously recorded by a side-by-side broadband seismometer. Moreover, seismological stations did not detect anything unusual, they presented a negative confirmation of the events. Our observation suggests that torsion balances might effectively detect precursory earthquake signals from a considerable distance. Such a finding could trigger the development of new observational devices and networks and can provide novel knowledge about the origin and mechanism of earthquake phenomena.

The motivation and research design for repeating the EPF experiments are described in the paper.

The accuracy of the classical heat conduction model, known as Fourier's law, is highly questioned, dealing with the micro- and nanosystems and biological tissues. In other words, the results obtained from the classical equations deviate from the available experimental data. It means that the continuum heat diffusion equation is insufficient and inappropriate for modeling heat transport in these cases. There are several techniques for modeling non-Fourier heat conduction. In the present paper, we place our focus on the dual-phase-lag (DPL) approach. The DPL model, as a popular modification of Fourier's law, has already been utilized in numerous situations, such as simulating ultrafast laser heating and heat conduction in carbon nanotubes. There has been a sharp increase in research on non-Fourier heat conduction in recent years. Several studies have been performed in the fields of thermoelasticity, thermodynamics, transistor modeling, and bioheat transport. This review presents the most recent non-Fourier bioheat conduction works and the related thermodynamics background. The various mathematical tools, modeling different thermal therapies, and relevant criticisms and disputes are discussed. Finally, the novel and other possible studies are also presented to provide a better overview, and the roadmap to the future research and challenges ahead is drawn up.

The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is similar to mode analysis in wave propagation. The new modal quantities characterise dissipation and best interpreted as effective diffusivities, or, in case of heat conduction, as effective heat conductivities of the material.

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.

Discovery of a novel thermodynamic aspect of nonrelativistic gravity is reported. Here, initially, an unspecified scalar field potential is considered and treated not as an externally applied field but as a thermodynamic variable on an equal footing with the fluid variables. It is shown that the second law of thermodynamics imposes a stringent constraint on the field, and, quite remarkably, the allowable field turns out to be only of gravity. The resulting field equation for the gravitational potential derived from the analysis of the entropy production rate contains a dissipative term due to irreversibility. It is found that the system relaxes to the conventional theory of Newtonian gravity up to a certain spatial scale, whereas on the larger scale there emerges non-Newtonian gravity described by a nonlinear field equation containing a single coefficient. A comment is made on an estimation of the coefficient that has its origin in the thermodynamic property of the system.

Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. The resulting field equation for the potential of this emergent force is nonlinear and admits the logarithmic potential as a singular solution, suggesting its relevance to the dark matter conundrum. Here, a general analysis of the nonlinear field equation is performed. It is found that the emergent force field exhibits an unsharp crossover between the 1/r and 1/r(2) forces outside the fluid, depending on a spatial scale characteristic of the present theory to be observationally tested in the context of the dark matter conundrum. Then, the action functional is constructed for the potential of the emergent field, and the field energy is shown to be free from an infrared divergence. A comment is also made on the difference of the present theory to MOND (modified Newtonian dynamics).