[論文レビュー] Non-equilibrium symmetry of cyclic first-passage times

Daniel Maria Busiello, Shiling Liang+1 more|arXiv (Cornell University)|Jan 26, 2026

Advanced Thermodynamics and Statistical Mechanics被引用数 0

ひとこと要約

この論文は、N>2 状態のサイクルに沿った循環的（時計回り対時計回り）一回通過時間の結合分布に対する詳細な揺らぎ定理を証明し、それをエントロピー生成と結びつけ、エントロピー生成の大偏差統計に接続します。

ABSTRACT

We study the sum of first passage times along an arbitrary cycle made up of N>2 states of a small physical system. We show that, if the system is at thermodynamic equilibrium, this sum follows the same probability distribution regardless of whether the cycle is explored clockwise or counterclockwise. Out of equilibrium, the distributions of clockwise and counterclockwise cyclic first passage times are related by a detailed fluctuation theorem. This result descends from a symmetry of clockwise and counterclockwise trajectories, which combines time reversal with swapping portions of the trajectories. We then relate the entropy produced along the cycle with the entropy production of the whole system using large deviation theory. Our results reveal a novel symmetry in stochastic systems, of potential broad applicability in non-equilibrium physics.

研究の動機と目的

• Motivate and define cyclic first-passage times along a closed path of N>2 states in a stationary Markovian system.
• Show that at thermodynamic equilibrium CW and CCW cyclic first-passage times share the same distribution.
• Derive a detailed fluctuation theorem linking CW and CCW distributions through entropy production.
• Relate the entropy production statistics of cycles to the overall entropy production via large deviation theory.
• Demonstrate the theory with an enzymatic cycle model and validate against simulations.

提案手法

• Define CW and CCW cyclic first-passage times as sums of single-step first-passage times around a closed loop.
• Prove a detailed fluctuation theorem p_CW(tau,s)/p_CCW(tau,-s)=e^{s} using a T.C (time reversal plus a trajectory-preserving operation) bijection.
• Introduce the C operators to map CW to CCW trajectories and prove equal counts of CW and cw trajectories within equivalence classes.
• Use large deviation theory to connect the cycle-level entropy production to the empirical entropy production rate via a Legendre transform and Gartner-Ellis framework.
• Derive expressions for the mean, variance, and third central moment of the entropy-production rate from the Laplace transform relation <e^{k_s s - psi(k_s) tau}> = 1.
• Apply to an enzymatic cycle with chemostatted substrates and nonequilibrium driving, validating the fluctuation theorem and cumulant relations.

実験結果

リサーチクエスチョン

• RQ1 Does the CW and CCW cyclic first-passage time distribution coincide at equilibrium?
• RQ2 What is the precise relationship between CW and CCW cyclic first-passage times out of equilibrium?
• RQ3 How does entropy production rate relate to cyclic first-passage time statistics via large deviation theory?
• RQ4 Can the theory be validated in a concrete biochemical cycle model with driving?
• RQ5 What experimental signatures can identify nonequilibrium dissipation from cyclic first-passage statistics?

主な発見

• At equilibrium, CW and CCW cyclic first-passage time distributions are identical.
• Out of equilibrium, CW and CCW distributions obey a detailed fluctuation theorem relating p_CW(tau,s) and p_CCW(tau,-s).
• A bijection between CW and CCW trajectories exists within equivalence classes, ensuring equal counts in each class.
• The scaled cumulant generating function psi(k_s) for the entropy production rate satisfies a key relation derived from an optimization over cycle counts: <e^{k_s s - psi(k_s) tau}> = 1.
• Explicit expressions connect the empirical entropy production rate statistics (mean, variance, skewness) to moments of cycle-level s and tau via Eqs. (25)-(27).
• Numerical demonstration in an enzymatic cycle shows agreement with the fluctuation theorem and cumulant predictions.