Stochastic Thermodynamics with both Even and Odd Controlling Parameters

Shortcuts to isothermality inspired development of stochastic thermodynamics with both even and odd controlling parameters. was developed to understand nonequilibrium phenomena of small systems. It is found that the definition of heat and the microscopically reversible condition are incompatible for small systems with odd controlling parameters. 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 definition of 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.

Reference
[1] Geng Li, H. T. Quan and Z. C. Tu, Shortcuts to isothermality and nonequilibrium work relations, Phys. Rev. E 96, 012144 (2017)
[2] Geng Li and Z. C. Tu, Stochastic thermodynamics with odd controlling parameters, Phys. Rev. E 100, 012127 (2019)