Generalization of the Second Law for a Nonequilibrium Initial State

TL;DR

This paper extends the second law of thermodynamics to include nonequilibrium initial states, linking maximum work, relative entropy, and information, with implications for small systems and experimental tests.

Contribution

It introduces a generalized second law applicable to nonequilibrium initial states, connecting work, entropy, and information in a unified framework.

Findings

Relative entropy bounds maximum work in nonequilibrium processes

The relation applies to small Hamiltonian systems with effective temperature

Testable in laboratory Szilard engine experiments

Abstract

We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function but also tells us the maximum work that may be gained from a nonequilibrium initial state. The generalized second law also gives a fundamental relation between work and information. It is valid even for a small Hamiltonian system not in contact with a heat reservoir but with an effective temperature determined by the isentropic condition. Our relation can be tested in the Szilard engine, which will be realized in the laboratory.