Related papers: Concavity, Response Functions and Replica Energy
We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be…
Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic,…
Ensemble inequivalence, i.e. the possibility of observing different thermodynamic properties depending on the statistical ensemble which describes the system, is one of the hallmarks of long-range physics, which has been demonstrated in…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
For macroscopic systems, the second law of thermodynamics establishes an inequality between the amount of work performed on a system in contact with a thermal reservoir, and the change in its free energy. For microscopic systems, this…
Active Brownian engines rectify energy from reservoirs composed of self-propelling non-equilibrium molecules into work. We consider a class of such engines based on an underdamped Brownian particle trapped in a power-law potential. The…
We derive a formula that defines quantum fluctuations of energy in subsystems of a hot relativistic gas. For small subsystem sizes we find substantial increase of fluctuations compared to those known from standard thermodynamic…
We compute for various perturbed conformal field theories the vacuum energies by means of the thermodynamic Bethe ansatz. Depending on the infrared and ultraviolet divergencies of the models, governed by the scaling dimensions of the…
We consider the one-dimensional driven ABC model under particle-conserving and particle-non-conserving processes. Two limiting cases are studied: (a) the rates of the non-conserving processes are vanishingly slow compared with the…
It is shown that there is a mapping of the replica approach to disordered systems with finite replica index $n$ on the Tsallis non-extensive statistics, if the average thermodynamic entropy differs from the information entropy for the…
We consider strictly increasing sequences $\left(a_{n}\right)_{n \geq 1}$ of integers and sequences of fractional parts $\left(\left\{a_{n} \alpha\right\}\right)_{n \geq 1}$ where $\alpha \in \mathbb{R}$. We show that a small additive…
In strongly interacting electron systems with low density and at low temperature the thermodynamic density of states is negative. It creates difficulties with understanding of the Einstein relation between conductivity and diffusion…
In this work we investigate the convergence to equilibrium for mass action reaction-diffusion systems which model irreversible enzyme reactions. Using the standard entropy method in this situation is not feasible as the irreversibility of…
We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and…
We investigate a solvable model for energy conserving non-equilibrium steady states. The time-reversal asymmetry of the dynamics leads to the violation of detailed balance and to ergodicity breaking, as manifested by the presence of…
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…
Standard results for the fluctuations of thermodynamic quantities are derived under the assumption of sampling identical systems that are in different, not fully equilibrated states. These results apply to fluctuations with time in a…
We discuss some physical consequences of the resurgent structure of Painleve equations and their related conformal block expansions. The resurgent structure of Painleve equations is particularly transparent when expressed in terms of…
The vacuum energy of a bosonic field interacting locally with objects is decomposed into irreducible $N$-body parts. The irreducible $N$-body contribution to the vacuum energy is finite if the common intersection $O_1\cap O_2...\cap O_N$ of…
We study the existence and the rate of equilibration of weak solutions to a two-component system of non-linear diffusion-aggregation equations, with small cross diffusion effects. The aggregation term is assumed to be purely attractive, and…