Related papers: The geometry of thermodynamic control

Boltzmann's principle S(E,N,V...)=ln W(E,N,V...) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E,N,V... (the conserved mechanical parameters in…

The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…

We present a review of the main aspects of geometrothermodynamics, an approach which allows us to associate a specific Riemannian structure to any classical thermodynamic system. In the space of equilibrium states, we consider a Legendre…

The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a…

We consider the motion planning of an object in a Riemannian manifold where the object is steered from an initial point to a final point utilizing optimal control. Considering Pontryagin Minimization Principle we compute the Optimal…

Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such…

From the perspective of the network theory, the present work illustrates how the parametric intrinsic geometric description exhibits an exact set of pair correction functions and global correlation volume with and without the inclusion of…

We construct a novel approach, based on thermodynamic geometry, to characterize first-order phase transitions from a microscopic perspective, through the scalar curvature in the equilibrium thermodynamic state space. Our method resolves key…

We investigate the consequences of reparametrizations in the geometric description of thermodynamics analyzing the effects on the thermodynamic phase space. It is known that the contact and Riemannian structures of the thermodynamic phase…

For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects,…

An earlier scheme [arXiv:2404.03360], where torsion plays an essential part in a flat spacetime account of fermion spin, is extended to spacetimes with non-zero Riemann curvature. It is found that further essential features of the fermion,…

In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of…

Thermoelectric metamaterials featuring width modulation through constrictions (constricted geometries) have emerged as a promising approach for improving heat management and thermoelectric performance. Through a combination of theoretical…

It is developed a Riemannian reformulation of classical statistical mechanics for systems in thermodynamic equilibrium, which arises as a natural extension of Ruppeiner geometry of thermodynamics. The present proposal leads to interpret…

We show that energy dissipation in slowly-driven, Markovian quantum systems at low temperature is linked to the geometry of the driving protocol through the quantum (or Fubini-Study) metric. Utilizing these findings, we establish lower…

We develop a geometric framework for irreversible transport phenomena in which macroscopic evolution equations arise from the combined structure of a thermodynamic state metric and an Onsager-based dissipation metric. The construction…

Developing the non-equilibrium thermodynamics of friction is required for systematic design of low friction surfaces for a broad range of technological applications. Intuitively, the thermodynamic work done by a material sliding along a…

We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…

A class of linear kinetic Fokker-Planck equations with a non-trivial diffusion matrix and with periodic boundary conditions in the spatial variable is considered. After formulating the problem in a geometric setting, the question of the…

Recently many results namely the Fluctuation theorems (FT), have been discovered for systems arbitrarily away from equilibrium. Many of these relations have been experimentally tested. The system under consideration is usually driven out of…