Related papers: Fourier's law and maximum path information
We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown…
We study the properties of heat conduction induced by non-Gaussian noises from athermal environments. We find that new terms should be added to the conventional Fourier law and the fluctuation theorem for the heat current, where its average…
We use nonequilibrium molecular dynamics (NEMD) to explore the effect of shear flow on heat flux. By simulating a simple fluid in a channel bounded by tethered atoms, the heat flux is computed for two systems: a temperature driven one with…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
For students familiar with equilibrium statistical mechanics, the notion of a positive specific heat, being intimately related to the idea of stability, is both intuitively reasonable and mathematically provable. However, for system in…
The action principle is introduced to describe the thermodynamic processes of the state functions from the initial equilibrium state to the final equilibrium state. To capture the path-independent property of the state functions through the…
Second law of thermodynamics can be apparently violated for systems whose dynamics depends on acquired information by measurement. However, when one consider measurement and erasure process together along with the system it saves the second…
A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the…
We review here {\it Maximum Caliber} (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of {\it Maximum Entropy} (Max…
Three different approaches to derive mutual information via thermodynamics are presented where the temperature-dependent energy is given by: (a) $\beta \mathcal{E} = -\ln[P(X,Y)]$, (b) $\beta \mathcal{E} =-\ln[P(Y|X)]$ or (c) $\beta…
For a small driven system coupled strongly to a heat bath, internal energy and exchanged heat are identified such that they obey the usual additive form of the first law. By identifying this exchanged heat with the entropy change of the…
Heat transport exhibits distinct regimes ranging from ballistic propagation to diffusive relaxation, traditionally described by disparate theoretical frameworks. Here, we introduce a unified first-order operator formulation in which…
I will discuss, from a dynamical systems point of view, some recent attempts to rigorously derive the macroscopic laws of transport (e.g. the heat equation) from deterministic microscopic dynamics.
We present a data-driven optimal control framework that can be viewed as a generalization of the path integral (PI) control approach. We find iterative feedback control laws without parameterization based on probabilistic representation of…
As an example for the optimization of unstable flows, we present an economics-based method for deciding the optimal rates at which vehicles are allowed to enter a highway. It exploits the naturally occuring fluctuations of traffic flow and…
Temperature-dependent transport data, including diffusion coefficients and ionic conductivities, are routinely analysed by fitting empirical models such as the Arrhenius equation. These fitted models yield parameters such as the activation…
We provide firm convincing evidence that the energy transport in a one-dimensional gas of elastically colliding free particles of unequal masses is anomalous, i.e. the Fourier Law does not hold. Our conclusions are based on the analysis of…
The dynamics of systems of many degrees of freedom evolving on multiple scales are often modeled in terms of stochastic differential equations. Usually the structural form of these equations is unknown and the only manifestation of the…
Heat conduction phenomena are studied theoretically using computer simulation. The systems are crystal with nonlinear interaction, and fluid of hard-core particles. Quasi-one-dimensional system of the size of $L_x\times L_y\times L_z(L_z\gg…
Dependence of hopping conductance on temperature and voltage for an ensemble of modestly long one-dimensional wires is studied numerically using the shortest-path algorithm. In a wide range of parameters this dependence can be approximated…