Related papers: The geometry of thermodynamic control
The fluctuations of spacetime geometries at finite temperature are evaluated within the linearized theory of gravity. These fluctuations are described by the probability distribution of various configurations of the gravitational field. The…
The systematic expansion method of the solution of the Fokker-Planck equation is developed by generalizing the formulation proposed in [J. Phys. A50, 325001 (2017)]. Using this method, we obtain a new formula to calculate the mean work…
The Riemannian geometry is one of the main theoretical pieces in Modern Mathematics and Physics. The study of Riemann Geometry in the relevant literature is performed by using a well defined analytical path. Usually it starts from the…
This work explores the role of the intrinsic fluctuations in finite parameter controller configurations characterizing an ensemble of arbitrary irregular filter circuits. Our analysis illustrates that the parametric intrinsic geometric…
This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…
We study horizontal differentiation when the set of feasible products is a structured subset of the Lancasterian characteristics space. Modeling this set as a compact Riemannian manifold, we show that intrinsic geometry governs…
Periodically driven coherent conductors provide a universal platform for the development of quantum transport devices. Here, we lay down a comprehensive theory to describe the thermodynamics of these systems. We first focus on moderate…
Progress in miniaturized technology allows us to control physical systems at nanoscale with remarkable precision. Experimental advancements have sparked interest in control problems in stochastic thermodynamics, typically concerning a…
Potential energy landscape (PEL) is essential to determine phase stability, reaction path, and other important physical as well as chemical properties. Whereas given PEL can reasonably determine the properties in thermodynamically…
Equilibrium phase transitions usually emerge from the microscopic behavior of many-body systems and are associated to interesting phenomena such as the generation of long-range order and spontaneous symmetry breaking. They can be defined…
Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
The solution to nonlinear Fokker-Planck equation is constructed in terms of the minimal Markov semigroup generated by the equation. The semigroup is obtained by a purely functional analytical method via Hille-Yosida theorem. The existence…
Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic…
We analyze the properties of foliations in presence of non-metricity, deriving the generalized Gauss-Codazzi relations in full generality. These results are employed to study the teleparallel framework of non-metric geometry, obtaining…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
We present the formalism of phenomenological thermodynamics in terms of the even-dimensional symplectic geometry, and argue that it catches its geometric essence in a more profound and clearer way than the popular odd-dimensional contact…
We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic…
Thermodynamic principles are often deceptively simple and yet surprisingly powerful. We show how a simple rule, such as the net flow of energy in and out of a moving atom under nonequilibrium steady state condition, can expose the…
This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…