Probabilities for informational free lunches in stochastic thermodynamics

TL;DR

This paper investigates the probability of violations of the second law of thermodynamics in a stochastic model, linking irreversibility, entropy production, and information deletion, challenging traditional thermodynamic principles.

Contribution

It introduces a probabilistic framework for second law violations and links information deletion to free lunches, extending stochastic thermodynamics insights.

Findings

Quantifies probability of second law violations under different initial conditions.

Relates irreversible entropy production to information deletion without work.

Provides a probabilistic perspective on Landauer's Principle.

Abstract

By considering an explicit nonequilibrium model, we analyze the statistics of the irreversible work, $w_{\rm irr}$, and irreversible entropy production, $\Delta_i s$, within the stochastic energetics framework. Restating the second law of thermodynamics as a function of $w_{\rm irr}$, we introduce the explicit probability of violating the canonical form of that second law for a different set of parameters and initial conditions of the model. Moreover, we study the irreversible entropy production along the same lines, since it can be cast as a generalization of the irreversible work. From an informational perspective, our result allows quantifying the probability of deleting information without performing work, contrarily to the Landauer's Principle, which we classify as an informational free lunch. We chose for initial conditions cases of low information content (equilibrium) and high information content (delta distributed).