Universal features in the energetics of symmetry breaking

Abstract

A symmetry breaking (SB) involves an abrupt change in the set of microstates that a system can explore. This change has unavoidable thermodynamic implications. According to Boltzmann's microscopic interpretation of entropy, a shrinkage of the set of compatible states implies a decrease of entropy, which eventually needs to be compensated by dissipation of heat and consequently requires work. Examples are the compression of a gas and the erasure of information. On the other hand, in a spontaneous SB, the available phase space volume changes without the need for work, yielding an apparent decrease of entropy. Here we show that this decrease of entropy is a key ingredient in the Szilard engine and Landauer's principle and report on a direct measurement of the entropy change along SB transitions in a Brownian particle. The SB is induced by a bistable potential created with two optical traps. The experiment confirms theoretical results based on fluctuation theorems, allows us to reproduce the Szilard engine extracting energy from a single thermal bath, and shows that the signature of a SB in the energetics is measurable, providing new methods to detect, for example, the coexistence of metastable states in macromolecules.When a symmetry is broken, a system "makes a choice" from among a set of instances i = 1, . . . , m. For a classical infinite system, symmetry breaking (SB) consists of a sudden change in the set of available states: the whole phase space Γ is partitioned into non-overlapping regions Γ i , corresponding to the different instances i = 1, . . . , m. The partition occurs when a certain control parameter λ crosses a critical value λ c above which the system can no longer move spontaneously from one region to another and gets confined within Γ i with probability p i , i p i = 1. The notion of SB can be extended to finite systems with metastable states. The confinement is not strict in this case: the system can jump form a region Γ i to another Γ j . However, if the average residence time in each region is much larger that the time scale of the pro- * Corresponding author: parrondo@fis.ucm.es cess under consideration, one can talk about an effective SB. In this case, the SB transition is not localized at a single value of the control parameter λ, but is rather a continuous transition where metastable states develop.The energetics associated to SB transitions and, in general, to the manipulation of metastable states has special relevance to a number of interesting physical situations, some of them realized experimentally in the last years. The original Szilard engine, a refined version of the original Maxwell demon, can extract work from a single thermal bath using the information created in a SB [1-4]. Landauer's principle accounts for the minimum dissipation associated to the erasure of information, which is a manipulation of the two metastable states making up a single bit memory [1]. The erasure can be interpreted as the restoration of a broken symmetry (see below) and has been reproduced with a Brownian...

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