A breaking of symmetry involves an abrupt change in the set of microstates a system can explore. This change has unavoidable thermodynamic implications: a shrinkage of the microstate set results in an entropy decrease, which eventually needs to be compensated by heat dissipation and hence requires work. On the other hand, in a spontaneous symmetry breaking, the available phase-space volume changes without the need for work, yielding an apparent entropy decrease. Here we show that this entropy decrease is a key ingredient of a Szilard engine and Landauer’s principle, and perform a direct measurement of the entropy change along symmetry-breaking transitions for a Brownian particle subject to a bistable potential realized through two optical traps. The experiment confirms theoretical results based on fluctuation theorems, enables the construction of a Szilard engine extracting energy from a single thermal bath, and shows that a signature of a symmetry breaking in a system’s energetics is observable.
At a glance
- 1990). & Maxwell’s Demon. Entropy, Information, Computing (Adam Hilger,
- The Szilard engine revisited: Entropy, macroscopic randomness, and symmetry breaking phase transitions. Chaos 11, 725–733 (2001).
- Cooling classical particles with a microcanonical Szilard engine. Phys. Rev. Lett. 104, 245704 (2010). &
- Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality. Nature Phys. 6, 988–992 (2010). , , , &
- Experimental verification of Landauer’s principle linking information and thermodynamics. Nature 483, 187–189 (2012). et al.
- A differential fluctuation theorem. J. Phys. Chem. B 112, 6168–6174 (2008). , &
- Recovery of free energy branches in single molecule experiments. Phys. Rev. Lett. 102, 070602 (2009). , , &
- Experimental free-energy measurements of kinetic molecular states using fluctuation theorems. Nature Phys. 8, 688–694 (2012). , , &
- Optimizing non-ergodic feedback engines. Acta. Phys. Pol. B 44, 803–814 (2013). &
- Minimal energy cost for thermodynamic information processing: Measurement and information erasure. Phys. Rev. Lett. 102, 250602 (2009). &
- Imitating chemical motors with optimal information motors. Phys. Rev. Lett. 111, 010602 (2013). , &
- Second law and Landauer principle far from equilibrium. Europhys. Lett. 95, 40004 (2011). &
- Nonequilibrium detailed fluctuation theorem for repeated discrete feedback. Phys. Rev. E 82, 061120 (2010). &
- Designing optimal discrete-feedback thermodynamic engines. New J. Phys. 13, 123019 (2011). &
- Dissipation: The phase-space perspective. Phys. Rev. Lett. 98, 080602 (2007). , &
- Phase transitions in small systems: Microcanonical vs. canonical ensembles. Physica A 370, 390–406 (2006). &
- Modeling Maxwell’s demon with a microcanonical Szilard engine. Phys. Rev. E 83, 061120 (2011). &
- Effective heating to several thousand kelvin of an optically trapped sphere in a liquid. Phys. Rev. E 87, 032159 (2013). , , &
- Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62, 251–342 (1990). , &
- Langevin equation and thermodynamics. Prog. Theor. Phys. Suppl. 130, 17–27 (1998).
- Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys. 75, 126001 (2012).
- Work and information processing in a solvable model of Maxwell’s demon. Proc. Natl Acad. Sci. USA 109, 11641–11645 (2012). &
- Realization of a micrometre-sized stochastic heat engine. Nature Phys. 8, 143–146 (2011). &
- Supplementary Information (746KB)