Thermal Casimir interactions for higher derivative field Lagrangians: generalized Brazovskii models

David S. Dean; Bing Miao; Rudolf Podgornik

Home/Archive/arXiv

arXiv · 2002.09822

Thermal Casimir interactions for higher derivative field Lagrangians: generalized Brazovskii models

David S. Dean·Bing Miao·Rudolf Podgornik

View original source ↗Read source document ↗Export metadata ↓

Abstract

We examine the Casimir effect for free statistical field theories which have Hamiltonians with second order derivative terms. Examples of such Hamiltonians arise from models of non-local electrostatics, membranes with non-zero bending rigidities and field theories of the Brazovskii type that arise for polymer systems. The presence of a second derivative term means that new types of boundary conditions can be imposed, leading to a richer phenomenology of interaction phenomena. In addition zero modes can be generated that are not present in standard first derivative models, and it is these zero modes which give rise to long range Casimir forces. Two physically distinct cases are considered: (i) unconfined fields, usually considered for finite size embedded inclusions in an infinite fluctuating medium, here in a two plate geometry the fluctuating field exists both inside and outside the plates, (ii) confined fields, where the field is absent outside the slab confined between the two plates. We show how these two physically distinct cases are mathematically related and discuss a wide range of commonly applied boundary conditions. We concentrate our analysis to the critical region where the underlying bulk Hamiltonian has zero modes and show that very exotic Casimir forces can arise, characterised by very long range effects and oscillatory behavior that can lead to strong metastability in the system.

Explore related subjects

cond-mat.stat-mech cond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

David S. Dean, Bing Miao, Rudolf Podgornik. 2020-02-23. Thermal Casimir interactions for higher derivative field Lagrangians: generalized Brazovskii models. https://arxiv.org/abs/2002.09822

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Far tails of the biased CTRW model under the short time limit

It has been observed in numerous experiments, simulations, and various theoretical studies that the spreading of particles can be modeled by the continuous-time random walk. We consider two widely used cases, namely Gaussian and discrete displacements, to compute the position distribution and demonstrate the emergence of exponential decay in the far tails when a bias is introduced. We further analyze the temporal rate function and the positional rate function to examine the convergence of the theoretical predictions. For Gaussian displacements, we also discuss the relationship between the position distributions with and without bias in different asymptotic limits.

cond-mat.stat-mech↗

arXiv2026

Stochastic Thermodynamics for Autoregressive Generative Models: A Non-Markovian Perspective

Autoregressive generative models -- including Transformers, recurrent neural networks, classical Kalman filters, state space models, and Mamba -- all generate sequences by sampling each output from a deterministic summary of the past, producing genuinely non-Markovian observed processes. We develop a general theoretical framework based on stochastic thermodynamics for this class of architectures and introduce the entropy production, which can be efficiently estimated from sampled trajectories without exponential sampling cost, despite the non-Markovian nature of the observed dynamics. As a proof-of-concept experiment with a large language model (LLM), we evaluate the entropy production for a pre-trained Transformer-based model, GPT-2. We find that the token-level entropy production is dominated by a syntactic artifact, while the sentence-level entropy production tends to be larger for causally ordered than for non-causal text sets. This observation is supported by a re-evaluation with a substantially larger model, Qwen3-4B-Base. We also demonstrate the framework in the linear Gaussian case, where the model reduces to the Kalman innovation representation and the entropy production admits an analytical expression. We also show that the entropy production decomposes exactly into non-negative per-step contributions in terms of retrospective inference, and each of those terms further splits into information-theoretically meaningful terms: a compression loss and a model mismatch. Our results establish a bridge between stochastic thermodynamics and modern generative models, and provide a starting point for using irreversibility as a quantitative probe of the highly non-Markovian processes generated by models such as LLMs.

cond-mat.stat-mech↗

arXiv2026

Quantum tunneling Mpemba effect

We investigate a quantum tunneling Mpemba effect for a particle in a continuous one-dimensional symmetric double-well potential subject to irreversible boundary loss. The dissipation is described by a complex absorbing potential (CAP) and the corresponding conditional no-jump evolution. Using a biorthogonal spectral representation, we derive the exact non-Hermitian decomposition of the subnormalized density matrix and analyze the corresponding relaxation dynamics. We show that the off-diagonal coefficients exhibit a parity selection rule, leaving same-parity interference terms in general. To isolate the interplay between thermal spectral preparation and mode-dependent decay rates, we introduce a diagonal spectral relaxation measure $S(t,T_i)$. For a quartic double well, numerical calculations reveal finite-time crossings of $S(t,T_i)$ prepared at different initial temperatures, as well as a non-monotonic temperature dependence of selected diagonal spectral weights. These features are explained by the enhanced thermal population of spatially extended, rapidly leaking excited states. In contrast, the trace distance of the normalized conditional state to the asymptotic quasi-stationary state exhibits no crossing, demonstrating that the anomalous ordering is specifically a spectral Mpemba effect rather than a universal acceleration of the complete conditional state. Our continuous-space formulation provides a real-space perspective on anomalous quantum relaxation without invoking universal nodal or topological theorems.

cond-mat.stat-mech↗