Derivation of the not-so-common fluctuation theorems

Abstract

The detailed fluctuation theorems of the exact form $P(A)/P(-A)=e^A$ exist only for a handful of variables $A$, namely for work (Crooks theorem), for total entropy change (Seifert's theorem), etc. However, the so-called modified detailed fluctuation theorems can be formulated for several other thermodynamic variables as well. The difference is that the modified relations contain an extra factor, which is dependent on $A$. This factor is usually an average of a quantity $e^{-B}$, where $B\ne A$, with repect to the conditional probability distribution $P(B|A)$. The corresponding modified integral fluctuation theorems also differ from their original counterparts, by not having the usual form $⟨e^{-A}⟩=1$. The generalization of these relations in presence of feedback has been discussed briefly. The results derived here serve to complement the already existing results in fluctuation theorems. The steps leading to the quantum version of these derivations have been outlined in the appendix.

References in corpus (10)

• Fluctuation theorems for stochastic dynamics
• Rare events and the convergence of exponentially averaged work values
• An Extension of the Fluctuation Theorem
• Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback
• Integral fluctuation theorem for the housekeeping heat
• Power and heat fluctuation theorems for electric circuits
• Fluctuation theorems in driven open quantum systems
• Fluctuation theorems for continuously monitored quantum fluxes
• Fluctuation Relation for Heat
• Fluctuation theorems for excess and housekeeping heats for underdamped systems

Cited by in corpus (8)

• Thermodynamic uncertainty relations from exchange fluctuation theorems
• Quantum fluctuation theorems beyond two-point measurements
• Jarzynski Equality, Crooks Fluctuation Theorem and the Fluctuation Theorems of Heat for Arbitrary Initial States
• Thermodynamic inference based on coarse-grained data or noisy measurements
• Transient exchange fluctuation theorems for heat using Hamiltonian framework: Classical and Quantum
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Extended Fluctuation Theorems for Repeated Measurements and Feedback within Hamiltonian Framework
• Heat exchange and fluctuation in Gaussian thermal states in the quantum realm