Variance sum rule: proofs and solvable models
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| Format: | Preprint |
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2024
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| author | Di Terlizzi, Ivan Baiesi, Marco Ritort, Felix |
| author_facet | Di Terlizzi, Ivan Baiesi, Marco Ritort, Felix |
| contents | We derive, in more general conditions, a recently introduced variance sum rule (VSR) [I. Di Terlizzi et al., 2024 Science 383 971] involving variances of displacement and force impulse for overdamped Langevin systems in a nonequilibrium steady state (NESS). This formula allows visualising the effect of nonequilibrium as a deviation of the sum of variances from normal diffusion $2Dt$, with $D$ the diffusion constant and $t$ the time. From the VSR, we also derive formulas for the entropy production rate $σ$ that, differently from previous results, involve second-order time derivatives of position correlation functions. This novel feature gives a criterion for discriminating strong nonequilibrium regimes without measuring forces. We then apply and discuss our results to three analytically solved models: a stochastic switching trap, a Brownian vortex, and a Brownian gyrator. Finally, we compare the advantages and limitations of known and novel formulas for $σ$ in an overdamped NESS. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_10442 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variance sum rule: proofs and solvable models Di Terlizzi, Ivan Baiesi, Marco Ritort, Felix Statistical Mechanics Soft Condensed Matter We derive, in more general conditions, a recently introduced variance sum rule (VSR) [I. Di Terlizzi et al., 2024 Science 383 971] involving variances of displacement and force impulse for overdamped Langevin systems in a nonequilibrium steady state (NESS). This formula allows visualising the effect of nonequilibrium as a deviation of the sum of variances from normal diffusion $2Dt$, with $D$ the diffusion constant and $t$ the time. From the VSR, we also derive formulas for the entropy production rate $σ$ that, differently from previous results, involve second-order time derivatives of position correlation functions. This novel feature gives a criterion for discriminating strong nonequilibrium regimes without measuring forces. We then apply and discuss our results to three analytically solved models: a stochastic switching trap, a Brownian vortex, and a Brownian gyrator. Finally, we compare the advantages and limitations of known and novel formulas for $σ$ in an overdamped NESS. |
| title | Variance sum rule: proofs and solvable models |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2403.10442 |