Fluctuation-optimization theorem

Pierre Nazé

Home/Archive/arXiv

arXiv · 2407.01243

Fluctuation-optimization theorem

Pierre Nazé

View original source ↗Read source document ↗Export metadata ↓

Abstract

A fluctuation theorem relating the work to its optimal average work is presented. The function mediating the relation is increasing and convex, and depends on the switching time $τ$, driving strength $δλ/λ_0$, and protocol $g(t)$. The result is corroborated by an example of an overdamped white noise Brownian motion subjected to a moving laser harmonic trap. Observing also that the fluctuation-optimization theorem is an Euler-Lagrange equation, I conclude that the function minimizing $\langle h(-βW)\rangle$ obeys the relation proposed. The optimal work can now be calculated with numerical methods without knowing the optimal protocol, using only a work distribution of an arbitrary protocol.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Pierre Nazé. 2024-07-01. Fluctuation-optimization theorem. https://arxiv.org/abs/2407.01243

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The free energy of the square lattice Ising model with interactions alternating in horizontal and vertical directions

The free energy of the Ising model on the square lattice with alternating interactions in both horizontal and vertical directions is exactly derived. This model is distinct from the checkerboard Ising model. The result includes Onsager's free energy as a special case, and also includes Lee-Yang's free energy with an imaginary field, and relates these two solutions via continuous parameters. The result includes a generalization of Lee-Yang's result to cases with four different couplings. It is also derived that each imaginary magnetic field $iπ/2$ applied to a lattice site corresponds to a single frustrated square in its dual lattice.

cond-mat.stat-mech↗

arXiv2026

Ideal heat engine cycles at maximal efficiency -- the ideal gas and beyond

Given a particular heat engine cycle, what is the optimal working medium that results in the highest efficiency? While one might jump to the conclusion that it must surely be the ideal gas, the situation is actually more intricate. Starting with a general Helmholtz potential that depends polynomially on molar volume and temperature we derive exact expressions for the ideal Stirling, Otto, and Brayton cycles. We find that for the thermodynamic systems described by our ansatz for the Helmholtz potential the maximal efficiency is achieved, if the working medium is described by a fundamental relation linear in temperature. This includes the ideal gas, but also classical harmonic oscillators and phenomenological models of the rubber band.

cond-mat.stat-mech↗

arXiv2026

Local Detailed Balance in the Lorenz Model: Replaces the Butterfly with Frenetic Bursting

The Lorenz system is the canonical low-order model of convective instability, yet its dissipative and driving terms have never been checked against, nor constructed from, an explicit thermodynamic bookkeeping. We derive a modification that satisfies the local-detailed-balance condition for macroscopic relaxation toward nonequilibrium steady states, thereby identifying the thermodynamic force, entropy-production rate and frenesy of the resulting flow. The resulting model produces a transition from a quiescent fixed point to a robust, large-amplitude relaxation oscillation, closely analogous to recharge-discharge oscillator paradigms used for the El Nino-Southern Oscillation. The system alternates between a long, nearly reversible recharge phase and a brief, violently frenetic discharge burst, during which essentially all of the cycle's activity and entropy production is concentrated.

cond-mat.stat-mech↗