Stochastic thermodynamics with odd controlling parameters

Abstract

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 in the current framework of stochastic thermodynamics. Herein, we apply stochastic thermodynamics to small systems with odd controlling parameters and find that the definition of heat and the microscopically reversible condition are incompatible. Such a contradiction also leads to a revision to the fluctuation theorems and nonequilibrium work relations. By introducing adjoint dynamics, we find that the total entropy production can be separated into three parts, with two of them satisfying the integral fluctuation theorem. Revising the definitions of work and heat and the microscopically reversible condition allows us to derive two sets of modified nonequilibrium work relations, including the Jarzynski equality, the detailed Crooks work relation, and the integral Crooks work relation. We consider the strategy of shortcuts to isothermality as an example and give a more sophisticated explanation for the Jarzynski-like equality derived from shortcuts to isothermality.

References in corpus (34)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Path ensembles averages in systems driven far-from-equilibrium
• Steady State Thermodynamics of Langevin Systems
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• The Fluctuation Theorem as a Gibbs Property
• Three detailed fluctuation theorems
• The Three Faces of the Second Law: I. Master Equation Formulation
• The Three Faces of the Second Law: II. Fokker-Planck Formulation
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Integral fluctuation theorem for the housekeeping heat
• Entropy production and fluctuation theorems for active matter
• Entropy production in full phase space for continuous stochastic dynamics
• Escorted Free Energy Simulations: Improving Convergence by Reducing Dissipation
• Experimental test of the differential fluctuation theorem and a generalized Jarzynski equality for arbitrary initial states
• Non-equilibrium thermodynamics of stochastic systems with odd and even variables
• Fluctuation Theorems of Brownian Particles Controlled by a Maxwell's Demon
• Shortcuts to isothermality and nonequilibrium work relations
• Entropy Production of Brownian Macromolecules with Inertia
• Fluctuation theorems in general stochastic processes with odd-parity variables
• The modified Sutherland--Einstein relation for diffusive nonequilibria
• Nonequilibrium Work distributions for a trapped Brownian particle in a time dependent magnetic field
• Jarzynski Equality, Crooks Fluctuation Theorem and the Fluctuation Theorems of Heat for Arbitrary Initial States
• Entropy and density of states from isoenergetic nonequilibrium processes
• The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping
• Hamiltonian derivation of a detailed fluctuation theorem
• Entropy production from stochastic dynamics in discrete full phase space
• A generalized integral fluctuation theorem for diffusion processes
• Housekeeping Entropy in Continuous Stochastic Dynamics with Odd-Parity Variables

Cited by in corpus (10)

• Geodesic path for the minimal energy cost in shortcuts to isothermality
• Unified formalism for entropy productions and fluctuation relations
• A microscopic theory of Curzon-Ahlborn heat engine
• Instantaneous equilibrium Transport for Brownian systems under time-dependent temperature and potential variations: Reversibility, Heat and work relations, and Fast Isentropic process
• Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
• The Statistical Foundation of Entropy in Extended Irreversible Thermodynamics
• Geodesic path for the optimal nonequilibrium transition: Momentum-independent protocol
• Time-Asymmetric Fluctuation Theorem and Efficient Free Energy Estimation
• A Shortcut to Finite-time Memory Erasure
• A minimal model with stochastically broken reciprocity