Related papers: On a nonhierarchical version of the generalized ra…
Recently we introduced a new technique for computing the average free energy of a system with quenched randomness. The basic tool of this technique is a distributional zeta-function. The distributional zeta-function is a complex function…
An expression is derived for the classical free energy difference between two configurations of a system, in terms of an ensemble of finite-time measurements of the work performed in parametrically switching from one configuration to the…
Within the framework of natural configurations developed by Rajagopal and Srinivasa, evolution within continuum thermodynamics is formulated as evolution of a natural configuration linked with the current configuration. On the other hand,…
In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of…
In this note, we explore the thermodynamic properties of the universe in the background of the generalized energy-momentum-squared gravity. We derive the energy density of matter from the non-standard continuity equation and use it in our…
We introduce an information free energy for thermodynamic systems driven by external time-dependent parameters. We show that the latter is a nonequilibrium state function and that it is a natural generalization of the usual equilibrium and…
In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…
We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power beta by the Vandermonde) to all orders of 1/N expansion in the case where the limiting eigenvalue…
We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side…
The free energy landscape of mean field marginal glasses is ultrametric. We demonstrate that this feature remains in finite three dimensional systems by finding sets of minima which are nearby in configuration space. By calculating the…
By using a previously established exact characterization of the ground state of random potential systems in the thermodynamic limit, we determine the ground and first excited energy levels of quantum random energy models, discrete and…
Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic…
An estimate on the operator norm of an abstract fermionic renormalization group map is derived. This abstract estimate is applied in another paper to construct the thermodynamic Green's functions of a two dimensional, weakly coupled fermion…
Nonequilibrium dynamics of a nonintegrable system without the eigenstate thermalization hypothesis is studied. It is shown that, in the thermodynamic limit, this model thermalizes after an arbitrary quantum quench at finite temperature,…
We study a random resistors network model on a euclidean geometry $\bt{Z}^d$. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per…
This paper explores the non-equilibrium behavior of thermodynamics at the apparent horizon of isotropic and homogeneous universe model in $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ represent the Gauss-Bonnet invariant and trace of…
The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be…
The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows to systematically improve the spectrum obtained…
We present and discuss the two-generator framework of nonequilibrium thermodynamics known as GENERIC ("general equation for the nonequilibrium reversible-irreversible coupling"), which is based on geometric concepts and on statistical…
We give a conjecture on the lower bound of the ADM mass $M$ by using the null energy condition. The conjecture includes a Penrose-like inequality $3M\geq\kappa\mathcal{A}/(4\pi)+\sqrt{\mathcal{A}/4\pi}$ and the Penrose inequality $…