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In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent…

In this paper, a theory for systems in contact with a thermal reservoir is developed. We call such systems "thermostated systems." Interest in these systems has been vigorous for about the last 20 years and is illustrated by the Crooks…

It is shown that the work fluctuations and work distribution functions are fundamentally different in systems with short-range versus long-range correlations. The two cases considered with long- range correlations are magnetic work…

We extend the framework of forward and reverse processes commonly utilized in the derivation and analysis of the nonequilibrium work relations to thermodynamic processes with repeated discrete feedback. Within this framework, we derive a…

Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin…

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time…

Graham has shown in Z. Physik B 26, 397-405 (1977) that a fluctuation-dissipation relation can be imposed on a class of non-equilibrium Markovian Langevin equations that admit a stationary solution of the corresponding Fokker-Planck…

The characteristic function for the joint measurement of the changes of two commuting observables upon an external forcing of a quantum system is derived. In particular, the statistics of the internal energy, the exchanged heat and the work…

Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived…

Firstly the fluctuation theorems (FT) for expended work in a driven nonequilibrium system, isolated or thermostatted, together with the ensuing Jarzynski work-energy (W-E) relationships, will be discussed and reobtained. Secondly, the…

Stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems that experience strong fluctuations. The definitions of work and heat and the microscopically reversible condition are two key concepts…

We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the…

We consider bosons in a harmonic trap and investigate the fluctuations of the work performed by an adiabatic change of the trap curvature. Depending on the reservoir conditions such as temperature and chemical potential that provide the…

In this work, we propose two models of coupled harmonic oscillators under Brownian motion to computationally study the applications of fluctuation theorems. This paper also illustrates how to analytically calculate free energy differences…

Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly…

Recent progress on micro- and nanometer scale manipulation has opened the possibility to probe systems small enough that thermal fluctuations of energy and coordinate variables can be significant compared with their mean behavior. We…

We probe the validity of Crooks' fluctuation relation on the fluctuating lattice-Boltzmann model (FLBM), a highly simplified lattice model for a thermal ideal gas. We drive the system between two thermodynamic equilibrium states and compute…

We show how Jarzynski relation can be exploited to analyze the nature of order-disorder and a bifurcation type dynamical transition in terms of a response function derived on the basis of work distribution over non-equilibrium paths between…

Fluctuation theorems, such as the Jarzynski equality and the Crooks relation, are effective tools connecting non-equilibrium work statistics and equilibrium free energy differences. However, detailed hands-on, reproducible protocols for…

The Jarzynski relation is a recently discovered result relating the average exponential of the work done under nonequilibrium conditions to an equilibrium free energy difference. We illustrate this remarkable relation by considering the…