A Universal Thermodynamic Inequality: Scaling Relations Between Current, Activity, and Entropy Production

TL;DR

This paper establishes a universal thermodynamic inequality linking current, activity, and entropy production, providing fundamental bounds on transport efficiency in nonequilibrium systems, applicable to both discrete and continuous models.

Contribution

It introduces a universal inequality connecting velocity, activity, and entropy production, unifying discrete and continuous stochastic thermodynamics.

Findings

Derived a fundamental inequality for nonequilibrium systems.

Unifies discrete and continuous thermodynamic relations.

Provides experimentally accessible bounds on transport efficiency.

Abstract

We derive a universal thermodynamic bound constraining directional transport in both discrete and continuous nonequilibrium systems. For continuous-time Markov jump processes and overdamped diffusions governed by Fokker--Planck equations, we prove the inequality $ \frac{2 V(t)^2}{A(t)} \leq \dot{e}_p(t), $ linking the squared net velocity $V(t)$, entropy production rate $\dot{e}_p(t)$, and dynamical activity $A(t)$. This relation captures a fundamental trade-off between transport, dissipation, and fluctuation intensity, valid far from equilibrium and without detailed balance. In addition, we introduce dimensionless thermodynamic ratios that quantify dissipation asymmetry, entropy extraction, and relaxation. These scaling laws unify discrete and continuous stochastic thermodynamics and provide experimentally accessible constraints on transport efficiency in nanoscale machines and active systems.