Thermodynamic work of partial resetting

Thermodynamic work of partial resetting

20 Jun 2024 | Kristian Stølevik Olsen, Deepak Gupta
This paper investigates the thermodynamic work associated with partial resetting in non-equilibrium steady states (NESS). Partial resetting, where a state variable $ x(t) $ is reset at random times to $ ax(t) $ with $ 0 \leq a \leq 1 $, generalizes conventional resetting by introducing the resetting strength $ a $. The study focuses on the thermodynamic cost of maintaining such NESS, considering resetting processes mediated by a resetting potential $ \Phi(x) $ that mediates resets in finite time. The work required to sustain the resulting NESS is analyzed, revealing that different resetting traps can lead to varying dependencies of the work rate on $ a $. Notably, for a harmonic trap, the asymptotic work rate is independent of $ a $, while for anharmonic traps, the rate can increase or decrease with $ a $, depending on the degree of anharmonicity. The work rate can also become negative in certain cases, depending on the relative strengths of the exploration and resetting potentials. The study also considers the work in the presence of a background potential and confirms findings through numerical simulations. The results highlight the importance of understanding the thermodynamic cost of partial resetting in various trapping scenarios.This paper investigates the thermodynamic work associated with partial resetting in non-equilibrium steady states (NESS). Partial resetting, where a state variable $ x(t) $ is reset at random times to $ ax(t) $ with $ 0 \leq a \leq 1 $, generalizes conventional resetting by introducing the resetting strength $ a $. The study focuses on the thermodynamic cost of maintaining such NESS, considering resetting processes mediated by a resetting potential $ \Phi(x) $ that mediates resets in finite time. The work required to sustain the resulting NESS is analyzed, revealing that different resetting traps can lead to varying dependencies of the work rate on $ a $. Notably, for a harmonic trap, the asymptotic work rate is independent of $ a $, while for anharmonic traps, the rate can increase or decrease with $ a $, depending on the degree of anharmonicity. The work rate can also become negative in certain cases, depending on the relative strengths of the exploration and resetting potentials. The study also considers the work in the presence of a background potential and confirms findings through numerical simulations. The results highlight the importance of understanding the thermodynamic cost of partial resetting in various trapping scenarios.
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[slides and audio] Thermodynamic work of partial resetting