Exchange fluctuation theorems for a chain of interacting particles in presence of two heat baths

Abstract

The exchange fluctuation theorem for heat exchanged between two systems at different temperatures, when kept in direct contact, has been investigated by C. Jarzynski and D. K. Wójcik, in Phys. Rev. Lett. {\bf 92}, 230602 (2004). We extend this result to the case where two Langevin reservoirs at different temperatures are connected via a conductor made of interacting particles, and are subjected to an external drive or work source. The Langevin reservoirs are characterized by Gaussian white noise fluctuations and concomitant friction coefficients. We first derive the Crooks theorem for the ratio between forward and reverse paths, and discuss the first law in this model. Then we derive the modified detailed fluctuation theorems (MDFT) for the heat exchanged at each end. These theorems differ from the usual form of the detailed fluctuation theorems (DFT) in literature, due the presence of an extra multiplicative factor. This factor quantifies the deviation of our MFDT from the DFT. Finally, we numerically study our model, with only two interacting particles for simplicity.

7 pages, 5 figures

References in corpus (11)

• Heat Transport in low-dimensional systems
• Fluctuation theorems for stochastic dynamics
• An Extension of the Fluctuation Theorem
• Power and heat fluctuation theorems for electric circuits
• Fluctuation theorems for continuously monitored quantum fluxes
• Influence of measurements on the statistics of work performed on a quantum system
• Relevance of initial and final conditions for the Fluctuation Relation in Markov processes
• Two simple models of classical heat pumps
• Fluctuation Relation for Heat
• Exact fluctuation theorem without ensemble quantities
• Heat Fluctuations in Brownian Transducers

Cited by in corpus (7)

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• Transient exchange fluctuation theorems for heat using Hamiltonian framework: Classical and Quantum
• Additivity of multiple heat reservoirs in Langevin equation
• Operational characteristics of single particle heat engines and refrigerators with time asymmetric protocol
• Extended Fluctuation Theorems for Repeated Measurements and Feedback within Hamiltonian Framework
• Equilibrium free energy differences at different temperatures from a single set of nonequilibrium transitions
• Heat exchange and fluctuation in Gaussian thermal states in the quantum realm