Related papers: Martingales for physicists: A treatise on stochast…
The appeal of thermodynamics to problems outside physics is undeniable, as is the growing recognition of its apparent universality, yet in the absence of a rigorous formalism divorced from the peculiarities of molecular systems all attempts…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale stochastic processes. Here we reveal the martingale structure for a general thermodynamic functional…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
Stochastic thermodynamics is a framework for describing non-equilibrium processes at the level of fluctuating trajectories, where the state of a system evolves as a stochastic time series, allowing thermodynamic quantities such as work,…
We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the…
A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "macrostates" (e.g. sets of "microstates"), the consequence on…
This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the classical theory of partial differential…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
We investigate thermodynamics of general nonequilibrium processes stopped at stochastic times. We propose a systematic strategy for constructing fluctuation-theorem-like martingales for each thermodynamic functional, yielding a family of…
This tutorial investigates the convergence of statistical mechanics and learning theory, elucidating the potential enhancements in machine learning methodologies through the integration of foundational principles from physics. The tutorial…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
In this study, our effort is to introduce Tsallis thermostatistics in some details and to give a brief review of the magnetic systems which have been studied in the frame of this formalism.
This text is a survey of the general theory of stochastic processes, with a view towards random times and enlargements of filtrations. The first five chapters present standard materials, which were developed by the French probability school…
We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.
In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about…