相关论文: Dynamic Riemannian Geometry of the Ising Model
A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a…
A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear…
Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles…
A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a…
Controlling thermodynamic cycles to minimize the dissipated heat is a longstanding goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and…
The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols which minimize the energy dissipated to the environment. Computational models are a crucial tool in this…
Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technological tools approach thermodynamically determined limits of efficiency. In complex, fluctuating systems, like nanomagnetic bits, finding…
Active matter represents a class of non-equilibrium systems that constantly dissipate energy to produce directed motion. The thermodynamic control of active matter holds great potential for advancements in synthetic molecular motors,…
Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, both in nanotechnology and biology. Progress in computing optimal protocols has thus far been limited to either…
A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy…
It is known that the trajectory of an endoreversibly driven system with minimal dissipation is a geodesic on the equilibrium state space. Thereby, the state space is equipped with the Riemannian metric given by the Hessian of the free…
A simple, general and practically exact method is developed for the equilibrium properties of the macroscopic physical systems with translational symmetry. Applied to the Ising model in two and three dimension, a modest calculation gives…
Optimal control of stochastic systems plays a central role in nonequilibrium physics, with applications in the study of biological molecular motors and the design of single-molecule experiments. While exact analytic solutions to…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control…
We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…
The exact solution of the two-dimensional (2D) Ising model at an external magnetic field is derived by a modified Clifford algebraic approach. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic…