Focus on stochastic thermodynamics

Abstract

We introduce the thirty papers collected in this 'focus on' issue. The contributions explore conceptual issues within and around stochastic thermodynamics, use this framework for the theoretical modeling and experimental investigation of specific systems, and provide further perspectives on and for this active field.Over the last ten years, stochastic thermodynamics has evolved into a comprehensive framework for describing small driven systems using the notions of classical thermodynamics like work, heat and entropy production on the level of individual fluctuating trajectories as reviewed in [1][2][3][4]. The present 'focus on' selection reports on the latest developments and presents new perspectives in the field, both theoretical and experimental. The thirty articles featured in this collection can roughly be ordered into six, partially overlapping, groups.One original motivation for developing classical thermodynamics was to understand the laws governing heat engines and to optimize their performance. Within stochastic thermodynamics, these issues are explored for micro-and nano-sized engines which has led to new insight valid even for macroscopic engines. Calvo Hernandez et al discuss the role of a finite cycle-time and the inevitable dissipation coming with it in an approach that unifies heat engines and refrigerators for which they derive and discuss optimization criteria [5]. For such cyclic engines, Izumida and Okuda present a phenomenological theory along the lines of linear irreversible thermodynamics based on a local equilibrium assumption [6]. Sheng and Tu discuss a hidden symmetry and higher order constitutive relations for tightly coupled heat engines [7]. If a steady-state engine runs only for a finite time, output and input will be fluctuating quantities leading to the concept of stochastic efficiency that can be analyzed using a large deviation approach. Gingrich et al investigate the subtleties arising in time-asymmetric steady-state heat engines [8]. Proesmans and Van den Broeck investigate and illustrate stochastic efficiency with five case studies including examples of isothermal engines [9].Molecular motors and, more generally, all cellular and biochemical processes typically run under isothermal conditions. A paradigmatic motor is the F1-ATPase for which Toyabe and Muneyuki present experimental results studying the response of single molecules to an external torque [10]. Two theoretical papers deal with the efficiency of molecular motors. Schmitt et al discuss the interplay between a power-stroke mechanism and rectification of thermal fluctuations through ATP consumption [11]. Zuckermann et al explore the role of persistence for creating linear motion without spatial or temporal asymmetry [12]. Copolymerization against an external force shares some similarities with molecular motors. Gaspard investigates how the force-velocity relation, entropy production and other quantities depends on the type of polymerization and the presence of disorder [13]. Lahiri et al study kinetics and thermodyna...

Energetics of a driven Brownian harmonic oscillator

“…where A(ω) is defined in equation (13) and From equations ( 16) and ( 14) it follows that the steady-state average potential energy has the form…”

“…) where x(t) is given by equations ( 5)- (13). It is the work performed by the external force F (t) on the system in the time interval (τ 0 , τ 0 + τ ).…”

“…Recently, much theor etical development has improved our understanding of non-equilibrium thermodynamics, such as fluctuation theorems [2][3][4][5][6], which have been generalized both in classical and quantum statistical physics [2,[7][8][9][10]. Moreover, a number of important results have been obtained in the theory of stochastic thermodynamics [11][12][13]. These approaches are particularly relevant for small systems where thermal fluctuations cannot be neglected, such as colloidal particles, polymers, molecular motors, etc [14].…”