20 Jun 2024 | Kristian Stolevik Olsen1,* and Deepak Gupta2,3,†
The paper explores the thermodynamic work associated with partial resetting, a process where a state variable \( x(t) \) is reset to a value \( ax(t) \) at random times, with \( 0 \leq a \leq 1 \). This generalizes conventional resetting by introducing a resetting strength \( a \) as a parameter, generating a family of non-equilibrium steady states (NESS) that interpolates between conventional NESS at strong resetting (\( a = 0 \)) and a Gaussian distribution at weak resetting (\( a \to 1 \)). The authors study the thermodynamic work needed to maintain these NESS from a thermodynamic perspective, focusing on the resetting phase mediated by a resetting potential \( \Phi(x) \). By working in an ensemble of trajectories with a fixed number of resets, they derive the steady-state properties of the propagator and its moments. They find that different resetting traps can lead to widely different rates of work depending on the resetting strength \( a \). Notably, for a harmonic trap, the asymptotic rate of work is insensitive to \( a \), while for general anharmonic traps, the rate can be increasing or decreasing as a function of \( a \). The paper also considers the work in the presence of a background potential and confirms the findings through numerical simulations.The paper explores the thermodynamic work associated with partial resetting, a process where a state variable \( x(t) \) is reset to a value \( ax(t) \) at random times, with \( 0 \leq a \leq 1 \). This generalizes conventional resetting by introducing a resetting strength \( a \) as a parameter, generating a family of non-equilibrium steady states (NESS) that interpolates between conventional NESS at strong resetting (\( a = 0 \)) and a Gaussian distribution at weak resetting (\( a \to 1 \)). The authors study the thermodynamic work needed to maintain these NESS from a thermodynamic perspective, focusing on the resetting phase mediated by a resetting potential \( \Phi(x) \). By working in an ensemble of trajectories with a fixed number of resets, they derive the steady-state properties of the propagator and its moments. They find that different resetting traps can lead to widely different rates of work depending on the resetting strength \( a \). Notably, for a harmonic trap, the asymptotic rate of work is insensitive to \( a \), while for general anharmonic traps, the rate can be increasing or decreasing as a function of \( a \). The paper also considers the work in the presence of a background potential and confirms the findings through numerical simulations.