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Register a new userUniversal features in the energetics of symmetry breaking
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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 Boltzmanns 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 Landauers 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.
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By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [I. Dornic, textit{et al.} Phys. Rev. Lett. textbf{87}, 045701 (2001)], we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture up and down spins. In particular we show that for nonlinear voter models the exit probability (probability to end with all spins up when starting with an initial fraction $x$ of them) assumes a nontrivial shape. The change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics. Also the time needed to reach the final consensus state $T_N(x)$ has an anomalous nonuniversal dependence on $x$.
We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of 4 phases, for this system: (i) classical nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.
Spontaneous symmetry breaking (SSB) is a key concept in physics that for decades has played a crucial role in the description of many physical phenomena in a large number of different areas, like particle physics, cosmology, and condensed-matter physics. SSB is thus an ubiquitous concept connecting several, both high and low energy, areas of physics and many textbooks describe its basic features in great detail. However, to study the dynamics of symmetry breaking in the laboratory is extremely difficult. In condensed-matter physics, for example, tiny external disturbances cause a preference for the breaking of the symmetry in a particular configuration and typically those disturbances cannot be avoided in experiments. Notwithstanding these complications, here we describe an experiment, in which we directly observe the spontaneous breaking of the temporal phase of a driven system with respect to the drive into two distinct values differing by $pi$.
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We present a framework in which the transition between a many-body localised (MBL) phase and an ergodic one is symmetry breaking. We consider random Floquet spin chains, expressing their averaged spectral form factor (SFF) as a function of time in terms of a transfer matrix that acts in the space direction. The SFF is determined by the leading eigenvalues of this transfer matrix. In the MBL phase the leading eigenvalue is unique, as in a symmetry-unbroken phase, while in the ergodic phase and at late times the leading eigenvalues are asymptotically degenerate, as in a system with degenerate symmetry-breaking phases. We identify the broken symmetry of the transfer matrix, introduce a local order parameter for the transition, and show that the associated correlation functions are long-ranged only in the ergodic phase.
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